NoisyRollout
Collection
8 items
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Updated
•
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images
images listlengths 1
1
| problem
stringlengths 13
234
| answer
stringlengths 1
34
| id
int64 0
2.1k
| choices
sequencelengths 4
4
| ground_truth
stringclasses 4
values |
|---|---|---|---|---|---|
<image>Find x. Round to the nearest tenth, if necessary.
|
11
| 1,106 |
[
"8",
"9",
"10",
"11"
] |
D
|
|
<image>In the figure, the vertices of quadrilateral ABCD intersect square EFGH and divide its sides into segments with measures that have a ratio of 1:2. Find the ratio between the areas of ABCD and EFGH.
|
5:9
| 1,354 |
[
"1:4",
"1:2",
"5:9",
"1: \\sqrt 2"
] |
C
|
|
<image>Find the value of $f$ in the parallelogram
|
14
| 704 |
[
"14",
"18",
"36",
"56"
] |
A
|
|
<image>Find the value of the variable $y$ in the figure.
|
125
| 468 |
[
"55",
"115",
"125",
"135"
] |
C
|
|
<image>Find $m\angle S$
|
123
| 1,005 |
[
"68",
"80",
"123",
"125"
] |
C
|
|
<image>Find $x$ so that $ m \parallel n $.
|
13
| 1,811 |
[
"10",
"11",
"12",
"13"
] |
D
|
|
<image>Find $ m ∠RSU $ so that $ m \parallel n $.
|
124
| 1,861 |
[
"114",
"116",
"120",
"124"
] |
D
|
|
<image>Find $x$.
|
12
| 1,676 |
[
"6",
"9",
"12",
"15"
] |
C
|
|
<image>Find the perimeter of the $\triangle A B C,$ if $\triangle A B C \sim \triangle C B D, A D=5$, $C D=12,$ and $B C=31.2$
|
78
| 68 |
[
"32.5",
"72",
"78",
"187.2"
] |
C
|
|
<image>$\overline{AB}$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the diameter of the circle.
|
17
| 2,074 |
[
"8",
"8.5",
"15",
"17"
] |
D
|
|
<image>Find $\angle 10$
|
50
| 1,047 |
[
"50",
"80",
"100",
"160"
] |
A
|
|
<image>Find the measure of $\angle 7$ if $\overline{A B} \perp \overline{B C}$.
|
140
| 606 |
[
"110",
"120",
"130",
"140"
] |
D
|
|
<image>Find $m \widehat {CF}$.
|
80
| 973 |
[
"40",
"49",
"80",
"98"
] |
C
|
|
<image>$\overline{BC} \| \overline{DF}$. $AC=15$, $BD=3x-2$, $CF=3x+2$, and $AB=12$. Find $x$.
|
6
| 1,982 |
[
"3",
"4",
"5",
"6"
] |
D
|
|
<image>Each pair of polygons is similar. Find y
|
70
| 1,298 |
[
"70",
"80",
"100",
"150"
] |
A
|
|
<image>Find x.
|
12
| 1,548 |
[
"9",
"12",
"15",
"16"
] |
B
|
|
<image>Quadrilateral ABCD is a rectangle. If $m\angle ADB = 4x + 8$ and $m\angle DBA = 6x + 12$, find x.
|
7
| 1,023 |
[
"7",
"20",
"36",
"54"
] |
A
|
|
<image>Find $x$.
|
2
| 84 |
[
"1",
"2",
"3",
"4"
] |
B
|
|
<image>Find x
|
22
| 1,119 |
[
"22",
"24",
"43",
"68"
] |
A
|
|
<image>Find x. Assume that any segment that appears to be tangent is tangent.
|
13
| 1,873 |
[
"13",
"34",
"106",
"160"
] |
A
|
|
<image>Find the perimeter of quadrilateral ABCD.
|
40 + 14 \sqrt { 2 }
| 157 |
[
"27 + 14 \\sqrt { 2 }",
"40 + 14 \\sqrt { 2 }",
"27 + 28 \\sqrt { 2 }",
"40 + 28 \\sqrt { 2 }"
] |
B
|
|
<image>Find $EG$.
|
10
| 1,394 |
[
"5",
"6.5",
"10",
"13"
] |
C
|
|
<image>In $\triangle JLP$, $m \angle JMP=3 x-6$, $JK=3y-2$, and $LK=5y-8$. Find $LK$ if $\overline{PK}$ is a median.
|
7
| 1,286 |
[
"2",
"5",
"7",
"8"
] |
C
|
|
<image>Find $ST$.
|
5
| 1,435 |
[
"5",
"10",
"12",
"16"
] |
A
|
|
<image>Find the measure of the altitude drawn to the hypotenuse.
|
\sqrt { 612 }
| 850 |
[
"18",
"\\sqrt { 612 }",
"34",
"612"
] |
B
|
|
<image>Use parallelogram $ABCD$ to find $AB$
|
12
| 1,593 |
[
"6",
"12",
"18",
"115"
] |
B
|
|
<image>Find the area of the figure. Round to the nearest tenth if necessary.
|
39.4
| 1,663 |
[
"39.4",
"49.0",
"68.2",
"78.7"
] |
A
|
|
<image>Find $x$ if $\odot M \cong \odot N$.
|
9
| 1,100 |
[
"8",
"9",
"10",
"12"
] |
B
|
|
<image>Find x. Round side measures to the nearest tenth.
|
35.1
| 1,213 |
[
"16.4",
"18.0",
"32.0",
"35.1"
] |
D
|
|
<image>Find x.
|
2 \sqrt { 5 }
| 1,559 |
[
"2 \\sqrt { 2 }",
"3 \\sqrt { 2 }",
"2 \\sqrt { 5 }",
"3 \\sqrt { 5 }"
] |
C
|
|
<image>If $QT=11$, what is $QU$.
|
11
| 1,635 |
[
"7",
"8",
"11",
"16"
] |
C
|
|
<image>$a=14, b=48,$ and $c=50$ find $tanA$
|
0.29
| 273 |
[
"0.17",
"0.19",
"0.29",
"0.50"
] |
C
|
|
<image>Find $y$ so that the quadrilateral is a parallelogram
|
41
| 1,433 |
[
"9",
"20",
"21",
"41"
] |
D
|
|
<image>$\ln \odot K$, $ M N=16$ and $m \widehat{M N}=98$. Find the measure of $LN$. Round to the nearest hundredth.
|
8.94
| 8 |
[
"6.93",
"7.50",
"8.94",
"10.00"
] |
C
|
|
<image>In the figure, $QR \| TS$, $QT \| RS$, and $m \angle 1=131$. Find the measure of $\angle 6$.
|
131
| 1,045 |
[
"101",
"111",
"121",
"131"
] |
D
|
|
<image>Find the measure of $m∠C$.
|
70
| 2,017 |
[
"35",
"70",
"90",
"140"
] |
B
|
|
<image>Find x
|
7
| 1,533 |
[
"7",
"9",
"11",
"15"
] |
A
|
|
<image>Find $m \angle 2$.
|
39
| 1,763 |
[
"33",
"39",
"51",
"108"
] |
B
|
|
<image>If PR || WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find PQ
|
6
| 749 |
[
"5.5",
"6",
"8",
"11"
] |
B
|
|
<image>Find z.
|
12 \sqrt { 3 }
| 457 |
[
"6 \\sqrt { 3 }",
"12 \\sqrt { 3 }",
"18 \\sqrt { 2 }",
"36"
] |
B
|
|
<image>WXYZ is a parallelogram. Find $m \angle Y Z W$
|
115
| 49 |
[
"33",
"65",
"82",
"115"
] |
D
|
|
<image>Find $XZ$.
|
23
| 257 |
[
"5",
"15",
"23",
"35"
] |
C
|
|
<image>Find y.
|
10
| 347 |
[
"6",
"8",
"10",
"12"
] |
C
|
|
<image>Find the measure of $\angle 1$.
|
56
| 330 |
[
"56",
"66",
"76",
"86"
] |
A
|
|
<image>Find $x$.
|
60
| 45 |
[
"50",
"55",
"60",
"70"
] |
C
|
|
<image>Find the area of the figure.
|
150
| 744 |
[
"105",
"135",
"150",
"160"
] |
C
|
|
<image>In $\odot P, m \widehat{E N}=66$ and $m \angle G P M=89$ .
Find $m \angle G N M$
|
44.5
| 454 |
[
"44.5",
"66",
"89",
"155"
] |
A
|
|
<image>Find $x$ so that the quadrilateral is a parallelogram
|
3
| 962 |
[
"3",
"5",
"7",
"8"
] |
A
|
|
<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.
|
1520
| 229 |
[
"1064",
"1120",
"1520",
"1888.1"
] |
C
|
|
<image>Find $x$.
|
3
| 585 |
[
"2",
"3",
"4",
"5"
] |
B
|
|
<image>Find $y$.
|
3
| 1,490 |
[
"1",
"2",
"3",
"4"
] |
C
|
|
<image>WXYZ is a parallelogram. Find $m \angle X W Z$
|
65
| 1,801 |
[
"33",
"65",
"82",
"115"
] |
B
|
|
<image>Find x.
|
\frac { 15 \sqrt { 2 } } { 2 }
| 1,669 |
[
"\\frac { 15 } { 2 }",
"\\frac { 15 \\sqrt { 2 } } { 2 }",
"\\frac { 15 \\sqrt { 3 } } { 2 }",
"15 \\sqrt { 2 }"
] |
B
|
|
<image>Find $x$ in the figure.
|
34
| 434 |
[
"27.7",
"34",
"41.3",
"68"
] |
B
|
|
<image>Find the measure of $\angle 1$ if $m \angle D G F=53$ and $m \angle A G C=40$.
|
37
| 52 |
[
"37",
"40",
"50",
"53"
] |
A
|
|
<image>Find the measure of the altitude drawn to the hypotenuse.
|
3 \sqrt { 5 }
| 680 |
[
"\\sqrt { 3 }",
"\\sqrt { 5 }",
"3",
"3 \\sqrt { 5 }"
] |
D
|
|
<image>Chords $\overline{JF}$ and $\overline{BC}$ intersect at $K .$ If $B K=8$, $K C=12,$ and $K F=16,$ find $J K$
|
6
| 807 |
[
"6",
"12",
"15",
"18"
] |
A
|
|
<image>Find x.
|
32.2
| 1,682 |
[
"7.0",
"16.6",
"32.2",
"35.5"
] |
C
|
|
<image>Find the measure of $\angle 2$ if $m \angle D G F=53$ and $m \angle A G C=40$.
|
50
| 2,082 |
[
"37",
"40",
"50",
"53"
] |
C
|
|
<image>Find the rhombus of the kite.
|
240
| 2,052 |
[
"120",
"180",
"240",
"300"
] |
C
|
|
<image>Use rhombus XYZW with $m \angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\frac{5 a+1}{4}$
Find XZ
|
8
| 1,620 |
[
"2",
"4",
"8",
"16"
] |
C
|
|
<image>Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.
|
30.4
| 1,101 |
[
"25",
"28.5",
"30.4",
"50"
] |
C
|
|
<image>What is ED?
|
not enough information
| 1,637 |
[
"15",
"25",
"88.5",
"not enough information"
] |
D
|
|
<image>If $P T=y-3, P S=y+2, R S=12,$ and $Q S=16$
solve for $y$
|
\frac { 14 } { 3 }
| 1,925 |
[
"\\frac { 3 } { 14 }",
"\\frac { 2 } { 3 }",
"\\frac { 3 } { 2 }",
"\\frac { 14 } { 3 }"
] |
D
|
|
<image>The diagonals of rhombus FGHJ intersect at K.
If $m\angle FJH = 82$, find $m\angle KHJ$.
|
49
| 265 |
[
"15",
"33",
"49",
"82"
] |
C
|
|
<image>$\Delta EFG$ is equilateral, and $\overline{E H}$ bisects $\angle E$. Find $x$.
|
6
| 71 |
[
"5",
"6",
"7",
"8"
] |
B
|
|
<image>Find y
|
4 \sqrt { 3 }
| 1,383 |
[
"2 \\sqrt { 3 }",
"4",
"4 \\sqrt { 3 }",
"8"
] |
C
|
|
<image>Find x.
|
4 \sqrt { 13 }
| 1,097 |
[
"4 \\sqrt { 5 }",
"4 \\sqrt { 13 }",
"8 \\sqrt { 5 }",
"8 \\sqrt { 13 }"
] |
B
|
|
<image>Find the area of the figure.
|
54.9
| 1,824 |
[
"22.9",
"29.7",
"54.9",
"60"
] |
C
|
|
<image>ABCD is a rhombus. If EB = 9, AB = 12 and $m\angle ABD = 55$ . Find $m\angle BDA$
|
55
| 1,455 |
[
"9",
"12",
"20",
"55"
] |
D
|
|
<image>$\triangle LMN \cong \triangle QRS$. Find $y$.
|
50
| 1,430 |
[
"10",
"20",
"40",
"50"
] |
D
|
|
<image>For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.
|
\frac { 3 } { 2 }
| 108 |
[
"\\frac { 4 } { 9 }",
"\\frac { 2 } { 3 }",
"\\frac { 3 } { 2 }",
"\\frac { 9 } { 4 }"
] |
C
|
|
<image>Quadrilateral MNOP is a rhombus. Find $m\angle MRN $
|
90
| 849 |
[
"56",
"90",
"124",
"140"
] |
B
|
|
<image>Find x. Round the side measure to the nearest tenth.
|
8.3
| 614 |
[
"4.2",
"8.3",
"16.7",
"69.4"
] |
B
|
|
<image>Find x. Assume that segments that appear to be tangent are tangent.
|
9.6
| 597 |
[
"6",
"8",
"9.6",
"14.6"
] |
C
|
|
<image>Find the area of the figure in feet. Round to the nearest tenth, if necessary.
|
14.4
| 1,508 |
[
"14.4",
"16",
"28.8",
"32"
] |
A
|
|
<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.
|
164
| 1,796 |
[
"82",
"164",
"836",
"1448"
] |
B
|
|
<image>Find $m\angle K$
|
62
| 1,041 |
[
"62",
"72",
"116",
"160"
] |
A
|
|
<image>Find $m \angle 2$.
|
23
| 1,913 |
[
"23",
"55",
"63",
"125"
] |
A
|
|
<image>Find $z$ in the figure.
|
13.5
| 1,172 |
[
"13.5",
"14",
"14.5",
"15"
] |
A
|
|
<image>Find $x$.
|
11
| 608 |
[
"9",
"11",
"37",
"47"
] |
B
|
|
<image>Quadrilateral ABCD is a rectangle. Find y
|
5
| 1,910 |
[
"5",
"12",
"24",
"25"
] |
A
|
|
<image>Find the measure of $\angle 1$.
|
55
| 140 |
[
"33",
"45",
"54",
"55"
] |
D
|
|
<image>Refer to trapezoid $CDFG$ with median $\overline{HE}$. Let $\overline{WX}$ be the median of $CDEH$. Find $WX$.
|
42
| 537 |
[
"34",
"38",
"42",
"46"
] |
C
|
|
<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear
to be tangent are tangent.
|
5
| 263 |
[
"5",
"10",
"15",
"20"
] |
A
|
|
<image>Find the area of the shaded region.
|
50.3
| 2,087 |
[
"12.6",
"50.3",
"100.5",
"402.1"
] |
B
|
|
<image>For trapezoid $R S T V, A$ and $B$ are midpoints of the legs. Find $V T$.
|
4
| 745 |
[
"4",
"8",
"26",
"30"
] |
A
|
|
<image>Find AX if $E X=24$ and $D E=7$
|
24
| 478 |
[
"1",
"7",
"24",
"25"
] |
C
|
|
<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.
|
315.2
| 1,409 |
[
"80.0",
"157.6",
"315.2",
"364.0"
] |
C
|
|
<image>What is the area of the triangle? Round your answer to the nearest tenth if necessary.
|
161.3
| 1,601 |
[
"137.4",
"161.3",
"170.5",
"186.9"
] |
B
|
|
<image>Find $m \angle K$.
|
46
| 930 |
[
"46",
"63",
"69",
"92"
] |
A
|
|
<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.
|
106.1
| 1,345 |
[
"75",
"106.1",
"150",
"212.1"
] |
B
|
|
<image>Find $y$ in the figure.
|
15
| 406 |
[
"15",
"34",
"67",
"75"
] |
A
|
|
<image>For trapezoid $D E G H, X$ and $Y$ are midpoints of the legs. Find $D E$
|
8
| 2,056 |
[
"8",
"16",
"20",
"32"
] |
A
|
|
<image>Find x.
|
24 \sqrt { 2 }
| 2,044 |
[
"24",
"24 \\sqrt { 2 }",
"36",
"24 \\sqrt { 3 }"
] |
B
|
|
<image>In $\odot F$, find $m \widehat {ADB}$.
|
243
| 286 |
[
"63",
"153",
"233",
"243"
] |
D
|
|
<image>Find the perimeter of the figure. Round to the nearest tenth if necessary.
|
54.8
| 934 |
[
"54.8",
"60",
"80",
"109.6"
] |
A
|
|
<image>In the figure, $ \overline{JM} \cong \overline{PM}$ and $ \overline{ML} \cong \overline{PL}$. If $m \angle PLJ=34$, find $m \angle JPM$.
|
36.5
| 782 |
[
"34",
"34.5",
"36",
"36.5"
] |
D
|
|
<image>The segment is tangent to the circle. Find $x$.
|
4
| 1,579 |
[
"3",
"4",
"5",
"8"
] |
B
|
|
<image>Find the radius of $\odot K$. Round to the nearest hundredth.
|
19.00
| 2,069 |
[
"9.50",
"19.00",
"56.37",
"59.69"
] |
B
|
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