Question

Show that the angles of an equilateral triangle are 60° each.

Answer 1

Let us consider that ABC is an equilateral triangle.

Therefore, AB = BC = AC AB = AC 

∠C =∠ B (Angles opposite to equal sides of a triangle are equal)

Also, 

Ac = BC 

∠B = ∠A (Angles opposite to equal sides of a triangle are equal) 

Therefore, we obtain A 

= ∠B = ∠C 

In ∆ABC, 

∠A + ∠B + C = 180° 

∠A + ∠A +∠A = 180° 

∠3A = 180° 

∠A = 60° 

∠A = ∠B = ∠C = 60° 

Hence, in an equilateral triangle, all interior angles are of measure 60º.