Given to prove that each angle of the equilateral triangle is 60^o

Let us consider an equilateral triangle ABC

Such that,

AB = BC = CA

Now,

AB = BC

∠A = ∠C [i] (Opposite angles to equal sides are equal)

BC = AC

∠B = ∠A [ii[ (Opposite angles to equal sides are equal)

From [i] and [ii], we get

∠A = ∠B = ∠C [iii]

We know that,

Sum of all angles of triangles = 180^o

∠A + ∠B + ∠C = 180^o

∠A + ∠A + ∠A = 180^o

3∠A = 180^o

∠A =

= 60^o

Therefore, ∠A = ∠B = ∠C = 60^o

Hence, each angle of an equilateral triangle is 60^o.