Question

In an isosceles triangle, the equal angles are each twice the vertex angle. Find the vertex angle.

Answer 1

Let the vertex angle of the triangle be 'x'.

Then, equal angles will be 2x.

By angle sum property of a triangle :-

x° + 2x° +3x° = 180°

=> 6x° = 180°

=> x = 30.

Hence, vertex angle = 30° Ans

Regards

Kshitij

Answer 2

the vertex angle = x

the base angle = y

What we know:

2y + x = 180

y = 2x

2y + x = 180

2(2x) + x = 180

4x + x = 180

5x = 180

x = 36

Thus, the vertex angle is 36°