Question

Prove that measure of each angle of an equilateral triangle is 60⁰ . 

Answer 1

Let ∆ABC be an equilateral triangle, then we have

AB = BC = CA ...(i) 

∴ AB = BC 

∴ ∠C = ∠A ...(ii) [Angles opposite to equal sides are equal] 

 Also, BC = CA 

∴ ∠A = ∠B ...(iii) [Angles opposite to equal sides] 

 By (ii) & (iii) we get ∠A = ∠B = ∠C 

 Now in ∆ABC ∠A + ∠B + ∠C = 180⁰ 

⇒ 3∠A = 180⁰ [∴∠A = ∠B = ∠C] 

⇒ ∠A = 60⁰ = ∠B = ∠C