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

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

Formula Used/Theory:-

→ Angle sum property

Sum of all angles of triangle is 180°

→ Exterior angle is equal to sum of interior opposite angles

If exterior angle ∠ABX = 140°

That means exterior angle is opposite of ∠B

∴ ∠ABX = ∠A + ∠C

140° = 2∠A

∠A = = 70°

∠C = 70°

⇒ By angle sum property

∠A + ∠B + ∠C = 180°

70° + ∠B + 70° = 180°

∠B = 180° - 140° = 40°

Result:- The angles of triangle are 70°;70°;40°