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°
In an isoceles triangle top vertex is twice the of the sum of the base angle.find all the exterior angles of the triangle?
2 answers
I believe exterior angles are 180 - interior angles. Their sum is 360.