Let us consider,

ABC be an equilateral triangle

BC = AC = AB (Length of all sides is same)

∠A = ∠B = ∠C (Sides opposite to the equal angles are equal)

Also,

∠A + ∠B + ∠C = 180^o

3∠A = 180^o

∠A = 60^o

Therefore,

∠A = ∠B = ∠C = 60^o

Thus,

The angles of an equilateral triangle are 60^o each