Question

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

(a) 100°

(b) 120°

(c) 110°

(d) 130°

Answer 1

Let be isosceles triangle

Then

Now it is given that vertex angle is 2 times the sum of base angles

(As)

Now

(Property of triangle)

(Since, and )

Hence (b).