Question

In an isosceles triangle, if the vertex angle is thrice the sum of the base angles, then the measure of the vertex angle is ____.

• A. ${135}^{\circ }$
• B. ${140}^{\circ }$
• C. ${145}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is A ${135}^{\circ }$

Let ∆ABC be isosceles with base angles ∠B = ∠C and vertex angle ∠A.

Thus, as per the given data
∠A = 3 (∠B + ∠C)

By angle sum property of a triangle,
∠A + ∠B + ∠C = 180°
⇒ 3 (∠B + ∠C) + ∠B + ∠C = 180°
⇒ 4 (∠B + ∠C) = 180°
⇒ ∠B + ∠C = 45°

Thus, ∠A = 3 (∠B + ∠C) = 135°.