Question

Prove that measure of each angle of an equilateral triangle is ${60}^o$.

Answer 1

Let $△ABC$ be an equilateral triangle. Then,

$AB=BC=CA$

Since angles opposite to equal sides of a triangle are equal.

$AB=BC$ and $BC=CA$

$⟹\angle C=\angle A$ and $\angle A=\angle B$

$⟹\angle A=\angle B=\angle C$

But, $\angle A+\angle B+\angle C={180}^o$

Therefore, $3\angle A={180}^o$

$\angle A={60}^o$

Hence, $\angle A=\angle B=\angle C={60}^o$