Given: Our given triangle is isosceles triangle. Also, the vertex angle is twice the sum of the base angles

To find: Measures of angles of triangle.

It is given that that given triangle is isosceles triangle.

Let vertex angle be y and base angles be x each.

So by given condition,

y = 2(x + x)

∴ y = 4x

Also, We know that,

Sum of all angles in any triangle = 180°

∴ y + x + x = 180°

y +2x = 180°

4x + 2x = 180°

∴ 6x = 180°

x = 30°

∴ y = 4 × 30°

y = 120°

Hence, vertex angle is 120° and base angles are 30° each.