Question

In ∆ABC, if ∠A = ∠C, and exterior angle ABX = 140°, then find the angles of the triangle.

Answer 1

Given, ∠A = ∠C and exterior ∠ABX = 140°

Let ∠A = ∠C = x

According to the exterior angle property,

Exterior ∠B = Interior ∠A + Interior ∠C

⇒ 140° = x + x

⇒ 140° = 2x

⇒ x = `140^circ/2` = 70°

So, ∠A = ∠C = 70°

Now, ∠A + ∠B + ∠C = 180°  ...[Angle sum property of a triangle]

⇒ 70° + ∠B + 70° = 180°

⇒ ∠B + 140° = 180°

⇒ ∠B = 180° – 140°

⇒ ∠B = 40°

Hence, all the angles of the triangles are 70°, 40° and 70°.