Let ABC is an equilateral triangle

We know that all the angles in an equilateral triangle are equal.

Therefore,

∠A = ∠B = ∠C (i)

Now,

∠A + ∠B + ∠C = 180^o (Sum of all angles of a triangle)

∠A + ∠A + ∠A = 180^o

3∠A = 180^o

∠A =

= 60^o

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