In an isosceles triangle, the vertex angle is twice the sum of the base angles. Find the angles of the triangle.

Question

Philoid · Accepted Answer

In a triangle ABC, let ∠A be the vertex angle and ∠C and ∠B be the base angles. It is given that

∠B = ∠C {∵ it is an isosceles triangle}

And ∠A = 2(∠B + ∠C)

⇒ ∠A = 2× 2 ∠B

∠A = 4 ∠B

We know that the sum of the angles of a triangle is 180°.

⇒ 4∠B + ∠B + ∠B = 180°

⇒ 6∠B = 180 °

⇒ ∠B = 30°

So, ∠C = ∠B = 30°

And ∠A = 4× ∠B = 120°