Question

Find all the angles of an equilateral triangle.

Answer 1

Let ABC be an equilateral triangle such that AB = BC = CA

We have, AB = AC ⇒ ∠C = ∠B  ...[Angle opposite to equal sides are equal]

Let ∠C = ∠B = x°  ...(i)

Now, BC = BA

⇒ ∠A = ∠C  ...(ii)  [Angles opposite to equal sides are equal]

From equations (i) and (ii),

∠A = ∠B = ∠C = x

Now, in ΔABC, ∠A + ∠B + ∠C = 180°  ...[By angle sum property of a triangle]

⇒ x + x + x = 180°

⇒ 3x = 180°

∴ x = 60°

Hence, ∠A = ∠B = ∠C = 60°