Question

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

Answer 1

Let ABC be an equilateral triangle.

∴ AB = BC = AC       …(A)

AB = BC               ...[Taking first and second terms]

⇒ ∠C = ∠A    …(i)      ...[Angles opposite to equal sides]

Therefore,

AB = AC                ...[Taking first and third terms of (A)]

⇒ ∠C = ∠B    …(ii)    ...[Angles opposite to equal sides]

From (i) and (ii) we get

∠A = ∠B = ∠C     …(iii)

Now in △ABC     …(iv)

∠A + ∠B + ∠C = 180°      ...[Angle Sum Property]

⇒ ∠A + ∠A + ∠A = 180°

⇒ 3∠A = 180

⇒ ∠A = 60°

From (iii), ∠A = ∠B = ∠C

⇒ ∠A = ∠B = ∠C = 60°

Hence, each angle of an equilateral triangle is 60°.