Question

In an isoceles triangle top vertex is twice the of the sum of the base angle.find all the exterior angles of the triangle?

Answer 1

If it is an isosceles triangle the two base angles will be equal.

Let the base angle be a, then the vertex angle will be:

180° - 2 a

According to the condition:

Top vertex is twice the of the sum of the base angle:

180° - 2 a = 2 ( a + a )

180° - 2 a = 2 * 2a

180° - 2 a = 4 a Add 2 a to both sides

180° - 2 a + 2 a = 4 a + 2 a

180° = 6 a Divide both sides by 6

180° / 6 = a

30° = a

a = 30 °

So the base angles are 30° and the vertex angle is 180° - 2 * 30° = 180° - 60° = 120 °

Exterior base angle is 360° - 30° = 330°

The exterior vertex angle is 360° - 120° = 240°

Answer 2

I believe exterior angles are 180 - interior angles. Their sum is 360.