What is the vertex angle if the base angle of an isosceles triangle is two more than five time the vertex angle?

Answer 1

If the vertex angle is x, then the two equal base angles are 5x + 2.

The sum of the angles of a triangle is 180 so:

x + 5x + 2 + 5x + 2 = 180

11x + 4 = 180

11x = 176

x = 16

vertex angle is 16 (and base angle are both 82)