Question

If the sides of a triangle are produced in an order, show that the sum of the exterior angles so formed is 360°.

Answer 1

In ΔABC, by exterior angle property,

Exterior ∠1 = Interior ∠A + Interior ∠B  ...(i)

Exterior ∠2 = Interior ∠B + Interior ∠C  ...(ii)

Exterior ∠3 = Interior ∠A + Interior ∠C  ...(iii)

On adding equations (i), (ii) and (iii), we get

∠1 + ∠2 + ∠3 = 2(∠A + ∠B + ∠C)  ...[By angle sum property of a triangle, ∠A + ∠B + ∠C = 180°]

⇒ ∠1 + ∠2 + ∠3 = 2 × 180°

⇒ ∠1 + ∠2 + ∠3 = 360°

Hence, the sum of exterior angles is 360°.