Yuting6/geoqa-concat-6k · Datasets at Hugging Face

images images listlengths 1 1	problem stringlengths 16 729	answer stringlengths 8 30
	<image>Question: In the given diagram, if angle 1 has a measure of 35.0 degrees, what is the measure of angle 2?	\boxed{145°}
	<image>Question: In the given diagram, consider right triangle ABC where angle C equals 90 degrees. The perpendicular bisector of side AB, labeled as DE, intersects BC at point D and intersects AB at point E. If AD divides angle CAB into two angles and the ratio of angle CAD to angle BAD is 0.4, what is the measure of angle ADC?	\boxed{75°}
	<image>Question: As shown in the figure, line l1 is parallel to line l2, and triangle ABC is an equilateral triangle. If angle 1 = 40°, then the size of angle 2 is ()	\boxed{80°}
	<image>Question: What is the measure of angle ADC in right triangle ABC if angle ACB is 90 degrees, angle A is 52 degrees, and a circle with point B as the center and BC as the radius intersects AB at point D?	\boxed{109°}
	<image>Question: What is the degree measure of angle CFA in triangle ABC, where AB is equal to AC, angle BAC measures 100°, AD is the median of side BC, CE bisects angle BCA, and intersects AB at point E, and AD intersects CE at point F?	\boxed{110°}
	<image>Question: In the given illustration, triangle ABC is depicted with BA being equal to BC. The line segment DE serves as the perpendicular bisector of side AB, intersecting BC and AB at points D and E, respectively. If AD functions as the angle bisector of angle BAC, what is the degree measure of angle B?	\boxed{36°}
	<image>Question: What is the measure of angle A in right triangle ABC, where angle ACB is 90 degrees, and an arc is drawn with point B as the center and BC as the radius, intersecting AB at point D, and angle ACD measures 20 degrees?	\boxed{50°}
	<image>Question: In the provided figure, the quadrilateral ABCD is inscribed in circle O. If one of its exterior angles, DCE, measures 62.0, what is the measure of angle BOD?	\boxed{124°}
	<image>Question: If a student utilizes a set square with acute angles measuring 30 degrees and 45 degrees and aligns the right-angled vertices, and angle DEB is 60 degrees, what is the measure of angle AOC?	\boxed{45°}
	<image>Question: In the given figure, point O is the intersection of AE and CD, with AB being parallel to CD. If OC is equal to OE and angle A measures 50 degrees, what is the measure of angle C?	\boxed{25°}
	<image>Question: If AB is parallel to CD and AC equals BC, and angle 1 measures 70 degrees in the given diagram, what is the degree measure of angle 2?	\boxed{40°}
	<image>Question: In the given diagram, point D lies on AC, while point E lies on AB. It is also given that AB is equal to AC, and BC is equal to BD, and AD is equal to DE, which also equals BE. What is the measure of angle A?	\boxed{45}
	<image>Question: What is the sum of angle A, angle B, angle C, angle D, angle E, and angle F in the given equation?	\boxed{360°}
	<image>Question: When Xiaoming was folding a rectangular piece of paper into a regular pentagon, what is the measure of angle 1 in the figure?	\boxed{72°}
	<image>Question: As shown in the diagram, the sides CD and FG of the regular pentagon ABCDE and the regular hexagon EFGHMN are on the line l. The pentagon is on the left side of the hexagon, and both polygons are on the same side of the line l. Therefore, the size of angle DEF is ().	\boxed{48°}
	<image>Question: Given that points A, B, and C lie on circle O and angle AOB measures 80.0 degrees, what is the measure of angle ACB?	\boxed{40°}
	<image>Question: As shown in the figure, pentagon ABCDE is a regular pentagon. If l1parallel l2, the value of angle 1 - angle 2 is ()	\boxed{72°}
	<image>Question: If points D and E are the midpoints of the sides AB and AC of triangle ABC and connected, and angle B measures 50 degrees while angle A measures 60 degrees, what is the degree measure of angle AED?	\boxed{70°}
	<image>Question: As shown in the figure, in ABCD, angle ADC = 135° and angle CAD = 23°, then angle CAB is equal to ().	\boxed{22°}
	<image>Question: In the given diagram depicting quadrilateral ABCD, if angle ABC measures 125 degrees and angle CAD measures 21 degrees, what is the measure of angle CAB?	\boxed{34°}
	<image>Question: What is the measure of angle E in triangle BCDE if angle A in triangle ABC measures 40 degrees and AB is equal to AC?	\boxed{70°}
	<image>Question: In the given diagram, if in triangle ABC, point D is the midpoint of AC and point E is the midpoint of AB, and point F lies on the extension of BC, and if angle A measures 35° and angle AED measures 30°, then what is the degree measure of angle ACF?	\boxed{65°}
	<image>Question: In the given diagram of quadrilateral ABCD, the angle bisector BE intersects DC at point E. If angle A measures 60°, what is the measure of angle DEB?	\boxed{120°}
	<image>Question: As shown in the figure, in ABCD, BD = BC, AE is perpendicular to BD, and the foot is E. If angle C = 55°, then the degree of angle EAB is ().	\boxed{35°}
	<image>Question: What is the measurement of angle B in parallelogram ABCD if the sum of angles A and C is 130 degrees, as depicted in the diagram?	\boxed{115°}
	<image>Question: If angle B in the parallelogram ABCD is 70 degrees, what is the measure of angle D?	\boxed{70°}
	<image>Question: In the given diagram, if the sum of angles A and C in parallelogram ABCD equals 160°, what is the measure of angle B?	\boxed{100°}
	<image>Question: In the given parallelogram ABCD, if the sum of angle B and angle D measures 100°, what is the measure of angle A?	\boxed{130°}
	<image>Question: In the given figure, if in quadrilateral ABCD, angle B added to angle D equals 140 degrees, what is the measure of angle C?	\boxed{110°}
	<image>Question: As shown in the diagram, in the parallelogram ABCD, angle DBC = 25°, angle BAD = 115°, then angle BDC = ().	\boxed{40°}
	<image>Question: If the sum of angle 2, angle 3, and angle 4 is 320.0 degrees as indicated in the figure, what is the measure of angle 1?	\boxed{40度}
	<image>Question: In the given parallelogram ABCD, if angle A measures 150 degrees, what is the degree measure of angle C?	\boxed{150°}
	<image>Question: In the given diagram illustrating quadrilateral ABCD, if the sum of angle B and angle D is 200 degrees, what is the measure of angle A?	\boxed{80°}
	<image>Question: In the given diagram of quadrilateral ABCD, where AB equals BD and point E lies on BD with CE measuring the same as CB, if angle ADB is 65 degrees, what would be the measure of angle DCE?	\boxed{15°}
	<image>Question: In the given diagram, for the quadrilateral ABCD, a point M is positioned on the extension of side AB. If angle D measures 120 degrees, what is the measure of angle CBM?	\boxed{60°}
	<image>Question: In the given figure, if the sum of angles A and C in quadrilateral ABCD is 110 degrees, what is the measure of angle B?	\boxed{125°}
	<image>Question: In the given figure for quadrilateral ABCD, if angle A measures twice the size of angle B, what is the measure of angle D?	\boxed{60°}
	<image>Question: What is the measure of angle D in parallelogram ABCD if the sum of angle A and angle C is 120 degrees, as depicted in the diagram?	\boxed{120°}
	<image>Question: If angle AOC is measured at 130.0 degrees in the figure depicting a set of triangular plates placed on a desktop (with the right-angle vertices coinciding), what is the measure of angle BOD?	\boxed{50°}
	<image>Question: In the given diagram of triangle ABC where AB is equal to AC, point D lies on side AC. By constructing quadrilateral BCDE with CB and CD as sides, if angle A measures 40°, what is the degree measure of angle E?	\boxed{70°}
	<image>Question: As shown in the diagram, extend one side of ABCD, BC, to point E. If angle 1 = 80°, then angle A is equal to ()	\boxed{100°}
	<image>Question: In the given diagram, the quadrilateral ABCD is depicted. If the measure of angle A is 100 degrees and BC is extended to point E, what is the measure of angle DCE?	\boxed{80°}
	<image>Question: If triangle ABC has angle B measuring 70 degrees and angle C measuring 50 degrees, and points D, E, and F are the midpoints of sides AB, BC, and CA respectively, what is the measure of angle DEF?	\boxed{60°}
	<image>Question: As shown in the figure, in ABCD, angle A+angle C=140°, then the measure of angle B is ().	\boxed{110°}
	<image>Question: In the provided figure, the perpendicular bisector of BC intersects AB and BC at point D and E, respectively. It also connects CD. If AC measures the same as DC and angle B is 25.0 degrees, what is the degree measure of angle ACD?	\boxed{80°}
	<image>Question: What is the measure of angle α when a set of protractors are stacked together as shown in the diagram?	\boxed{75°}
	<image>Question: As shown in the figure, if angle A = 20°, angle B = 45°, angle C = 35°, then angle DFE is equal to ().	\boxed{100°}
	<image>Question: In the given diagram, if triangle ABC is folded along DE and point A ends up outside quadrilateral BCDE, with angle 1 measuring 70° and angle 2 measuring 152°, what is the measure of angle A?	\boxed{42°}
	<image>Question: What is the measure of angle 2 if a triangle ruler with a 30.0 angle is placed on the ruler and angle 1 measures 25.0 degrees in the given figure?	\boxed{35°}
	<image>Question: As shown in the diagram, given angle A = 60°, the sum of the degrees of angle D + angle E + angle F + angle G is ()	\boxed{240°}
	<image>Question: In the given heptagon ABCDEFG, the lines EF and BA are extended to intersect at point P. If the total of the exterior angles of angles ABC, BCD, CDE, and DEF is 230°, what is the measurement of angle P?	\boxed{50°}
	<image>Question: In the provided diagram, if angle A measures 70°, angle B measures 40°, and angle C measures 30°, what is the total measure of angles D and E?	\boxed{40°}
	<image>Question: In the given diagram, points B, C, and D are aligned in a straight line. If angle B measures 56° and angle ACD measures 120°, what is the measure of angle A?	\boxed{64°}
	<image>Question: Triangle ABC's interior angle bisectors OB and OC intersect at point O. If angle A = 110°, then angle BOC = ()	\boxed{145°}
	<image>Question: What is the measure of angle α in the triangle board puzzle activity stacked by Xiaoming according to the given diagram?	\boxed{105°}
	<image>Question: In the given diagram, circle O has chord AB and tangent AC with point A as the tangent point. Additionally, line BC passes through the center of the circle. If angle B measures 25.0, what is the measure of angle C?	\boxed{40°}
	<image>Question: In the provided grid diagram, the vertices of triangle ABC are situated on the grid points, and the side length of each small square is 1. What is the measure of angle ABC?	\boxed{135°}
	<image>Question: In the given diagram, if BD is the diameter of circle O, and BD is perpendicular to AC at point E, with angle AOC measuring 100 degrees, what is the measure of angle OCD?	\boxed{25°}
	<image>Question: As shown in the figure, triangle ABC is circumscribed to circle O and angle A is 40°. Therefore, the degree of angle BCO is ()	\boxed{50°}
	<image>Question: In the given diagram, if angle C in circle O measures 20 degrees and angle B is 35 degrees, what is the measure of angle A?	\boxed{15°}
	<image>Question: In the given diagram, if triangle ABC is inscribed in circle O and the measure of angle ABO is 40 degrees, what is the measure of angle ACB?	\boxed{50°}
	<image>Question: If quadrilateral ABCD is circumscribed around circle O and one of its exterior angles, angle DCE, measures 115°, then what is the measure of the other exterior angle, angle DAF?	\boxed{65°}
	<image>Question: In the given diagram, all the points A, B, C, D, and P are located on the circle O. The line OC is perpendicular to AB. When angle ADC measures 15° (where 0° < α < 90°), what is the measure of angle APB?	\boxed{150°}
	<image>Question: In the given diagram, AB is the diameter of circle O, and points C and D lie on circle O. If angle D measures 120°, what is the measure of angle CAB?	\boxed{30°}
	<image>Question: If CD is the diameter of circle O and chord DE is parallel to radius OA, while arc CE measures 92 degrees, what is the measure of angle C?	\boxed{23°}
	<image>Question: If point A, B, and C are on circle O and angle B measures 32 degrees, what is the measure of angle OAC?	\boxed{58°}
	<image>Question: In the provided diagram, points A, B, and C lie on the circle O in the given order. If the difference between angle B and angle A is 40 degrees, what is the measure of angle AOB?	\boxed{80°}
	<image>Question: Given the figure with points A, B, C, D, and E all lying on circle O, and AC equal to AE, if angle B measures 128 degrees, what is the degree measure of angle D?	\boxed{104°}
	<image>Question: As shown in the diagram, point A, B, and C are three points on circle O. If angle AOB = 66°, then the degree of angle C is ()	\boxed{33°}
	<image>Question: In the given diagram, if quadrilateral ABCD is inscribed in circle O and angle BCD measures 140°, what is the degree measure of angle BOD?	\boxed{80°}
	<image>Question: Given that points A, B, and C all lie on circle O, and angle BOC measures 100 degrees, what is the measure of angle BAC?	\boxed{50°}
	<image>Question: As shown in the figure, AB is the diameter of circle O. C and D are two points on circle O. Connect AC, CD, and AD. If angle ADC = 75°, then the degree of angle BAC is ().	\boxed{15°}
	<image>Question: In the given diagram, circle O has line AB as its diameter. Point D lies on circle O, and OD and BD are connected. A tangent is drawn to circle O passing through point D, and it intersects the extension of line BA at point C. If angle C measures 40°, what is the measure of angle B?	\boxed{25°}
	<image>Question: As shown in the figure, quadrilateral ABCD is inscribed in circle O, with DA=DC. If angle CBE=45°, then the measure of angle DAC is ()	\boxed{67.5°}
	<image>Question: What is the measure of angle AOB if angle ACB measures 36 degrees and points A, B, and C are all located on circle O?	\boxed{72°}
	<image>Question: If in the given figure, circle O is the circumcircle of triangle ABC, and angle A measures 62°, and E is the midpoint of BC, what is the degree measure of angle D where OE, extended, intersects circle O at point D, and BD is then connected?	\boxed{59°}
	<image>Question: In the given diagram of circle O, if the length of AB is equal to the length of AC and angle B measures 70 degrees, what is the measure of angle A?	\boxed{40°}
	<image>Question: The degree of angle ADE is ().	\boxed{100°}
	<image>Question: Given that BD is the diameter of circle O and point A and C lie on the circle with CD equal to OB, what is the measure of angle BAC?	\boxed{60°}
	<image>Question: In the given diagram, quadrilateral ABCD is inscribed in circle O, and angle A measures 100 degrees. What is the measure of angle BOD?	\boxed{160°}
	<image>Question: If point A, B, and C lie on circle O and angle B measures 32 degrees, what is the measure of angle AOC?	\boxed{64°}
	<image>Question: In the given illustration, circle O has diameter AB, with points C and D situated on the circle. If angle BDC measures 36 degrees, what is the degree measurement of angle ABC?	\boxed{54°}
	<image>Question: In the given illustration, if BD serves as the diameter of circle O and is perpendicular to AC at point E, and angle AOC is 100 degrees, what is the measure of angle BDC?	\boxed{25°}
	<image>Question: In the given illustration, if points A, B, and C lie on circle O and the measure of angle AOB is 82 degrees, what is the degree measure of angle C?	\boxed{41°}
	<image>Question: What is the measure of angle D if AB is the diameter of circle O, and points C and D lie on circle O, with angle CAB equal to 20 degrees?	\boxed{110°}
	<image>Question: On circle O, points A, B, C, and D are positioned such that OA is perpendicular to BC at point E. If angle ADC measures 35°, what is the degree measure of angle OBC?	\boxed{20°}
	<image>Question: In the given diagram, it is depicted that AB serves as the diameter of circle O, and CD acts as a chord of circle O. If angle BAD measures 56°, what is the measurement of angle ACD?	\boxed{34°}
	<image>Question: In the given diagram, circle O shows radius OC being perpendicular to AB at point H. If angle OAB is 40 degrees, what is the measure of angle ABC?	\boxed{25°}
	<image>Question: In the given diagram, triangle ABC is inscribed in circle O with angle A measuring 50°. The midpoint of side BC is denoted by E. What is the measure of angle D formed when extending OE to intersect circle O at point D and connecting BD?	\boxed{65°}
	<image>Question: As shown in the picture, in circle O, AB is a diameter, and C and D are two points on circle O. OC is parallel to AD. If angle DAC = 25°, then the degree of angle BOC is ()	\boxed{50°}
	<image>Question: What is the measure of angle ADC if AB is the diameter of a semicircle and C, D are two points on the semicircle such that angle CAB measures 24 degrees?	\boxed{114°}
	<image>Question: As shown in the figure, in circle O, AB is the diameter, angle A = 50°, point D is the midpoint of chord AC, and point E is any point on BC. The possible size of angle CED is ().	\boxed{40°}
	<image>Question: In the given diagram, the line AB is a tangent to circle O at point A, while OB intersects circle O at point C, and point D lies on the major arc AC. If angle B measures 30 degrees, what is the degree measure of angle ADC?	\boxed{30°}
	<image>Question: In the figure, triangle ABC is circumscribed about circle O, AB=AC, BO is connected and extended to intersect AC at point D. If angle A=50°, then the measure of angle BDC is ().	\boxed{75°}
	<image>Question: If points A, B, C, and D lie on circle O, with AB equal to AC and BD being a diameter of circle O, and CD being connected, what is the measure of angle ACD if angle A measures 36°?	\boxed{18°}
	<image>Question: Given the diagram with circle O, if angle BOD measures 80 degrees, what is the measure of angle BCD?	\boxed{140°}
	<image>Question: In the given diagram, the line AB is tangent to circle O at point A, and the line OB intersects circle O at point C. Additionally, point D lies on circle O. If angle ABO is measured at 20 degrees, what is the degree measure of angle ADC?	\boxed{35°}
	<image>Question: What is the measure of angle APC if point P lies on line segment ED, and circle O is the circumcircle of the regular pentagon ABCDE?	\boxed{72°}
	<image>Question: In the provided diagram, circle O has diameter AB and point C lies on the circle. If angle OCA measures 25.0 degrees, what is the measure of angle BOC?	\boxed{50°}
	<image>Question: If PA and PB are tangents to circle O at points A and B, and C is a moving point on arc AB, what is the measure of angle ACB if angle P measures 40 degrees?	\boxed{70°}

<image>Question: In the given diagram, if angle 1 has a measure of 35.0 degrees, what is the measure of angle 2?

\boxed{145°}

<image>Question: In the given diagram, consider right triangle ABC where angle C equals 90 degrees. The perpendicular bisector of side AB, labeled as DE, intersects BC at point D and intersects AB at point E. If AD divides angle CAB into two angles and the ratio of angle CAD to angle BAD is 0.4, what is the measure of angle ADC?

\boxed{75°}

<image>Question: As shown in the figure, line l1 is parallel to line l2, and triangle ABC is an equilateral triangle. If angle 1 = 40°, then the size of angle 2 is ()

\boxed{80°}

<image>Question: What is the measure of angle ADC in right triangle ABC if angle ACB is 90 degrees, angle A is 52 degrees, and a circle with point B as the center and BC as the radius intersects AB at point D?

\boxed{109°}

<image>Question: What is the degree measure of angle CFA in triangle ABC, where AB is equal to AC, angle BAC measures 100°, AD is the median of side BC, CE bisects angle BCA, and intersects AB at point E, and AD intersects CE at point F?

\boxed{110°}

<image>Question: In the given illustration, triangle ABC is depicted with BA being equal to BC. The line segment DE serves as the perpendicular bisector of side AB, intersecting BC and AB at points D and E, respectively. If AD functions as the angle bisector of angle BAC, what is the degree measure of angle B?

\boxed{36°}

<image>Question: What is the measure of angle A in right triangle ABC, where angle ACB is 90 degrees, and an arc is drawn with point B as the center and BC as the radius, intersecting AB at point D, and angle ACD measures 20 degrees?

\boxed{50°}

<image>Question: In the provided figure, the quadrilateral ABCD is inscribed in circle O. If one of its exterior angles, DCE, measures 62.0, what is the measure of angle BOD?

\boxed{124°}

<image>Question: If a student utilizes a set square with acute angles measuring 30 degrees and 45 degrees and aligns the right-angled vertices, and angle DEB is 60 degrees, what is the measure of angle AOC?

\boxed{45°}

<image>Question: In the given figure, point O is the intersection of AE and CD, with AB being parallel to CD. If OC is equal to OE and angle A measures 50 degrees, what is the measure of angle C?

\boxed{25°}

<image>Question: If AB is parallel to CD and AC equals BC, and angle 1 measures 70 degrees in the given diagram, what is the degree measure of angle 2?

\boxed{40°}

<image>Question: In the given diagram, point D lies on AC, while point E lies on AB. It is also given that AB is equal to AC, and BC is equal to BD, and AD is equal to DE, which also equals BE. What is the measure of angle A?

\boxed{45}

<image>Question: What is the sum of angle A, angle B, angle C, angle D, angle E, and angle F in the given equation?

\boxed{360°}

<image>Question: When Xiaoming was folding a rectangular piece of paper into a regular pentagon, what is the measure of angle 1 in the figure?

\boxed{72°}

<image>Question: As shown in the diagram, the sides CD and FG of the regular pentagon ABCDE and the regular hexagon EFGHMN are on the line l. The pentagon is on the left side of the hexagon, and both polygons are on the same side of the line l. Therefore, the size of angle DEF is ().

\boxed{48°}

<image>Question: Given that points A, B, and C lie on circle O and angle AOB measures 80.0 degrees, what is the measure of angle ACB?

\boxed{40°}

<image>Question: As shown in the figure, pentagon ABCDE is a regular pentagon. If l1parallel l2, the value of angle 1 - angle 2 is ()

\boxed{72°}

<image>Question: If points D and E are the midpoints of the sides AB and AC of triangle ABC and connected, and angle B measures 50 degrees while angle A measures 60 degrees, what is the degree measure of angle AED?

\boxed{70°}

<image>Question: As shown in the figure, in ABCD, angle ADC = 135° and angle CAD = 23°, then angle CAB is equal to ().

\boxed{22°}

<image>Question: In the given diagram depicting quadrilateral ABCD, if angle ABC measures 125 degrees and angle CAD measures 21 degrees, what is the measure of angle CAB?

\boxed{34°}

<image>Question: What is the measure of angle E in triangle BCDE if angle A in triangle ABC measures 40 degrees and AB is equal to AC?

\boxed{70°}

<image>Question: In the given diagram, if in triangle ABC, point D is the midpoint of AC and point E is the midpoint of AB, and point F lies on the extension of BC, and if angle A measures 35° and angle AED measures 30°, then what is the degree measure of angle ACF?

\boxed{65°}

<image>Question: In the given diagram of quadrilateral ABCD, the angle bisector BE intersects DC at point E. If angle A measures 60°, what is the measure of angle DEB?

\boxed{120°}

<image>Question: As shown in the figure, in ABCD, BD = BC, AE is perpendicular to BD, and the foot is E. If angle C = 55°, then the degree of angle EAB is ().

\boxed{35°}

<image>Question: What is the measurement of angle B in parallelogram ABCD if the sum of angles A and C is 130 degrees, as depicted in the diagram?

\boxed{115°}

<image>Question: If angle B in the parallelogram ABCD is 70 degrees, what is the measure of angle D?

\boxed{70°}

<image>Question: In the given diagram, if the sum of angles A and C in parallelogram ABCD equals 160°, what is the measure of angle B?

\boxed{100°}

<image>Question: In the given parallelogram ABCD, if the sum of angle B and angle D measures 100°, what is the measure of angle A?

\boxed{130°}

<image>Question: In the given figure, if in quadrilateral ABCD, angle B added to angle D equals 140 degrees, what is the measure of angle C?

\boxed{110°}

<image>Question: As shown in the diagram, in the parallelogram ABCD, angle DBC = 25°, angle BAD = 115°, then angle BDC = ().

\boxed{40°}

<image>Question: If the sum of angle 2, angle 3, and angle 4 is 320.0 degrees as indicated in the figure, what is the measure of angle 1?

\boxed{40度}

<image>Question: In the given parallelogram ABCD, if angle A measures 150 degrees, what is the degree measure of angle C?

\boxed{150°}

<image>Question: In the given diagram illustrating quadrilateral ABCD, if the sum of angle B and angle D is 200 degrees, what is the measure of angle A?

\boxed{80°}

<image>Question: In the given diagram of quadrilateral ABCD, where AB equals BD and point E lies on BD with CE measuring the same as CB, if angle ADB is 65 degrees, what would be the measure of angle DCE?

\boxed{15°}

<image>Question: In the given diagram, for the quadrilateral ABCD, a point M is positioned on the extension of side AB. If angle D measures 120 degrees, what is the measure of angle CBM?

\boxed{60°}

<image>Question: In the given figure, if the sum of angles A and C in quadrilateral ABCD is 110 degrees, what is the measure of angle B?

\boxed{125°}

<image>Question: In the given figure for quadrilateral ABCD, if angle A measures twice the size of angle B, what is the measure of angle D?

\boxed{60°}

<image>Question: What is the measure of angle D in parallelogram ABCD if the sum of angle A and angle C is 120 degrees, as depicted in the diagram?

\boxed{120°}

<image>Question: If angle AOC is measured at 130.0 degrees in the figure depicting a set of triangular plates placed on a desktop (with the right-angle vertices coinciding), what is the measure of angle BOD?

\boxed{50°}

<image>Question: In the given diagram of triangle ABC where AB is equal to AC, point D lies on side AC. By constructing quadrilateral BCDE with CB and CD as sides, if angle A measures 40°, what is the degree measure of angle E?

\boxed{70°}

<image>Question: As shown in the diagram, extend one side of ABCD, BC, to point E. If angle 1 = 80°, then angle A is equal to ()

\boxed{100°}

<image>Question: In the given diagram, the quadrilateral ABCD is depicted. If the measure of angle A is 100 degrees and BC is extended to point E, what is the measure of angle DCE?

\boxed{80°}

<image>Question: If triangle ABC has angle B measuring 70 degrees and angle C measuring 50 degrees, and points D, E, and F are the midpoints of sides AB, BC, and CA respectively, what is the measure of angle DEF?

\boxed{60°}

<image>Question: As shown in the figure, in ABCD, angle A+angle C=140°, then the measure of angle B is ().

\boxed{110°}

<image>Question: In the provided figure, the perpendicular bisector of BC intersects AB and BC at point D and E, respectively. It also connects CD. If AC measures the same as DC and angle B is 25.0 degrees, what is the degree measure of angle ACD?

\boxed{80°}

<image>Question: What is the measure of angle α when a set of protractors are stacked together as shown in the diagram?

\boxed{75°}

<image>Question: As shown in the figure, if angle A = 20°, angle B = 45°, angle C = 35°, then angle DFE is equal to ().

\boxed{100°}

<image>Question: In the given diagram, if triangle ABC is folded along DE and point A ends up outside quadrilateral BCDE, with angle 1 measuring 70° and angle 2 measuring 152°, what is the measure of angle A?

\boxed{42°}

<image>Question: What is the measure of angle 2 if a triangle ruler with a 30.0 angle is placed on the ruler and angle 1 measures 25.0 degrees in the given figure?

\boxed{35°}

<image>Question: As shown in the diagram, given angle A = 60°, the sum of the degrees of angle D + angle E + angle F + angle G is ()

\boxed{240°}

<image>Question: In the given heptagon ABCDEFG, the lines EF and BA are extended to intersect at point P. If the total of the exterior angles of angles ABC, BCD, CDE, and DEF is 230°, what is the measurement of angle P?

\boxed{50°}

<image>Question: In the provided diagram, if angle A measures 70°, angle B measures 40°, and angle C measures 30°, what is the total measure of angles D and E?

\boxed{40°}

<image>Question: In the given diagram, points B, C, and D are aligned in a straight line. If angle B measures 56° and angle ACD measures 120°, what is the measure of angle A?

\boxed{64°}

<image>Question: Triangle ABC's interior angle bisectors OB and OC intersect at point O. If angle A = 110°, then angle BOC = ()

\boxed{145°}

<image>Question: What is the measure of angle α in the triangle board puzzle activity stacked by Xiaoming according to the given diagram?

\boxed{105°}

<image>Question: In the given diagram, circle O has chord AB and tangent AC with point A as the tangent point. Additionally, line BC passes through the center of the circle. If angle B measures 25.0, what is the measure of angle C?

\boxed{40°}

<image>Question: In the provided grid diagram, the vertices of triangle ABC are situated on the grid points, and the side length of each small square is 1. What is the measure of angle ABC?

\boxed{135°}

<image>Question: In the given diagram, if BD is the diameter of circle O, and BD is perpendicular to AC at point E, with angle AOC measuring 100 degrees, what is the measure of angle OCD?

\boxed{25°}

<image>Question: As shown in the figure, triangle ABC is circumscribed to circle O and angle A is 40°. Therefore, the degree of angle BCO is ()

\boxed{50°}

<image>Question: In the given diagram, if angle C in circle O measures 20 degrees and angle B is 35 degrees, what is the measure of angle A?

\boxed{15°}

<image>Question: In the given diagram, if triangle ABC is inscribed in circle O and the measure of angle ABO is 40 degrees, what is the measure of angle ACB?

\boxed{50°}

<image>Question: If quadrilateral ABCD is circumscribed around circle O and one of its exterior angles, angle DCE, measures 115°, then what is the measure of the other exterior angle, angle DAF?

\boxed{65°}

<image>Question: In the given diagram, all the points A, B, C, D, and P are located on the circle O. The line OC is perpendicular to AB. When angle ADC measures 15° (where 0° < α < 90°), what is the measure of angle APB?

\boxed{150°}

<image>Question: In the given diagram, AB is the diameter of circle O, and points C and D lie on circle O. If angle D measures 120°, what is the measure of angle CAB?

\boxed{30°}

<image>Question: If CD is the diameter of circle O and chord DE is parallel to radius OA, while arc CE measures 92 degrees, what is the measure of angle C?

\boxed{23°}

<image>Question: If point A, B, and C are on circle O and angle B measures 32 degrees, what is the measure of angle OAC?

\boxed{58°}

<image>Question: In the provided diagram, points A, B, and C lie on the circle O in the given order. If the difference between angle B and angle A is 40 degrees, what is the measure of angle AOB?

\boxed{80°}

<image>Question: Given the figure with points A, B, C, D, and E all lying on circle O, and AC equal to AE, if angle B measures 128 degrees, what is the degree measure of angle D?

\boxed{104°}

<image>Question: As shown in the diagram, point A, B, and C are three points on circle O. If angle AOB = 66°, then the degree of angle C is ()

\boxed{33°}

<image>Question: In the given diagram, if quadrilateral ABCD is inscribed in circle O and angle BCD measures 140°, what is the degree measure of angle BOD?

\boxed{80°}

<image>Question: Given that points A, B, and C all lie on circle O, and angle BOC measures 100 degrees, what is the measure of angle BAC?

\boxed{50°}

<image>Question: As shown in the figure, AB is the diameter of circle O. C and D are two points on circle O. Connect AC, CD, and AD. If angle ADC = 75°, then the degree of angle BAC is ().

\boxed{15°}

<image>Question: In the given diagram, circle O has line AB as its diameter. Point D lies on circle O, and OD and BD are connected. A tangent is drawn to circle O passing through point D, and it intersects the extension of line BA at point C. If angle C measures 40°, what is the measure of angle B?

\boxed{25°}

<image>Question: As shown in the figure, quadrilateral ABCD is inscribed in circle O, with DA=DC. If angle CBE=45°, then the measure of angle DAC is ()

\boxed{67.5°}

<image>Question: What is the measure of angle AOB if angle ACB measures 36 degrees and points A, B, and C are all located on circle O?

\boxed{72°}

<image>Question: If in the given figure, circle O is the circumcircle of triangle ABC, and angle A measures 62°, and E is the midpoint of BC, what is the degree measure of angle D where OE, extended, intersects circle O at point D, and BD is then connected?

\boxed{59°}

<image>Question: In the given diagram of circle O, if the length of AB is equal to the length of AC and angle B measures 70 degrees, what is the measure of angle A?

\boxed{40°}

<image>Question: The degree of angle ADE is ().

\boxed{100°}

<image>Question: Given that BD is the diameter of circle O and point A and C lie on the circle with CD equal to OB, what is the measure of angle BAC?

\boxed{60°}

<image>Question: In the given diagram, quadrilateral ABCD is inscribed in circle O, and angle A measures 100 degrees. What is the measure of angle BOD?

\boxed{160°}

<image>Question: If point A, B, and C lie on circle O and angle B measures 32 degrees, what is the measure of angle AOC?

\boxed{64°}

<image>Question: In the given illustration, circle O has diameter AB, with points C and D situated on the circle. If angle BDC measures 36 degrees, what is the degree measurement of angle ABC?

\boxed{54°}

<image>Question: In the given illustration, if BD serves as the diameter of circle O and is perpendicular to AC at point E, and angle AOC is 100 degrees, what is the measure of angle BDC?

\boxed{25°}

<image>Question: In the given illustration, if points A, B, and C lie on circle O and the measure of angle AOB is 82 degrees, what is the degree measure of angle C?

\boxed{41°}

<image>Question: What is the measure of angle D if AB is the diameter of circle O, and points C and D lie on circle O, with angle CAB equal to 20 degrees?

\boxed{110°}

<image>Question: On circle O, points A, B, C, and D are positioned such that OA is perpendicular to BC at point E. If angle ADC measures 35°, what is the degree measure of angle OBC?

\boxed{20°}

<image>Question: In the given diagram, it is depicted that AB serves as the diameter of circle O, and CD acts as a chord of circle O. If angle BAD measures 56°, what is the measurement of angle ACD?

\boxed{34°}

<image>Question: In the given diagram, circle O shows radius OC being perpendicular to AB at point H. If angle OAB is 40 degrees, what is the measure of angle ABC?

\boxed{25°}

<image>Question: In the given diagram, triangle ABC is inscribed in circle O with angle A measuring 50°. The midpoint of side BC is denoted by E. What is the measure of angle D formed when extending OE to intersect circle O at point D and connecting BD?

\boxed{65°}

<image>Question: As shown in the picture, in circle O, AB is a diameter, and C and D are two points on circle O. OC is parallel to AD. If angle DAC = 25°, then the degree of angle BOC is ()

\boxed{50°}

<image>Question: What is the measure of angle ADC if AB is the diameter of a semicircle and C, D are two points on the semicircle such that angle CAB measures 24 degrees?

\boxed{114°}

<image>Question: As shown in the figure, in circle O, AB is the diameter, angle A = 50°, point D is the midpoint of chord AC, and point E is any point on BC. The possible size of angle CED is ().

\boxed{40°}

<image>Question: In the given diagram, the line AB is a tangent to circle O at point A, while OB intersects circle O at point C, and point D lies on the major arc AC. If angle B measures 30 degrees, what is the degree measure of angle ADC?

\boxed{30°}

<image>Question: In the figure, triangle ABC is circumscribed about circle O, AB=AC, BO is connected and extended to intersect AC at point D. If angle A=50°, then the measure of angle BDC is ().

\boxed{75°}

<image>Question: If points A, B, C, and D lie on circle O, with AB equal to AC and BD being a diameter of circle O, and CD being connected, what is the measure of angle ACD if angle A measures 36°?

\boxed{18°}

<image>Question: Given the diagram with circle O, if angle BOD measures 80 degrees, what is the measure of angle BCD?

\boxed{140°}

<image>Question: In the given diagram, the line AB is tangent to circle O at point A, and the line OB intersects circle O at point C. Additionally, point D lies on circle O. If angle ABO is measured at 20 degrees, what is the degree measure of angle ADC?

\boxed{35°}

<image>Question: What is the measure of angle APC if point P lies on line segment ED, and circle O is the circumcircle of the regular pentagon ABCDE?

\boxed{72°}

<image>Question: In the provided diagram, circle O has diameter AB and point C lies on the circle. If angle OCA measures 25.0 degrees, what is the measure of angle BOC?

\boxed{50°}

<image>Question: If PA and PB are tangents to circle O at points A and B, and C is a moving point on arc AB, what is the measure of angle ACB if angle P measures 40 degrees?

\boxed{70°}