# CLASS-8GEOMETRY-TRIANGLE- PROBLEM & SOLUTION

TRIANGLE- PROBLEM & SOLUTION

Example.1) In a ∆ ABC, if ∠A = 75⁰,  ∠B = 90⁰, then find ∠C = ?

Ans.)  In ∆ ABC, ∠A + ∠B + ∠C = 180⁰

So, as per the given condition -

∠A + ∠B + ∠C = 180⁰

Or,  75⁰ + 90⁰ + ∠C = 180⁰

Or,  ∠C = 180⁰ - (75⁰ + 90⁰) =  180⁰ - 165⁰ =  15⁰      (Ans.)

Example.2) Prove that, each angle of an equilateral triangle is 60⁰

Ans.)  In the figure, XYZ in an equilateral angles

So, XY = YZ = ZX => ∠X = ∠Y = ∠Z

But, we know ∠X + ∠Y + ∠Z = 180⁰

Or,   ∠X + ∠X + ∠X = 180⁰

Or,     3 ∠X  =  180⁰

Or,    ∠X  =  180⁰/3 = 60⁰

Similarly,  ∠Y =  180⁰/3 = 60⁰

Similarly,  ∠Z =  180⁰/3 = 60⁰

Hence,  ∠X  =  ∠Y  =  ∠Z  =  60⁰                  (Ans.)

Example.3) Find BAC from the figure.

∠BCD => ∠BAC + ∠ABC = 125

=> ∠BAC + 65⁰ = 125

=> ∠BAC = 60⁰    (Ans.)
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