The base angle of an isosceles triangle is nine more than four times the vertex angle. What is the measure of the vertex angle?

Question

there's no photo its just the question..

Answer 1

Every isosceles triangle has two base angles that are equal.

Let the vertex angle be "x", then 4 times that is 4x and nine more than that is "4x + 9" so one of the base angles is 4x + 9.

The angles in a triangle add up to 180° so adding them all up and setting it equal to 180, we get:

(vertex angle) + (one base angle) + (the other base angle) = 180

(x) + (4x + 9) + (4x + 9) = 180

x + 4x + 9 + 4x + 9 = 180

9x + 18 = 180

9x = 162

x = 18

So the vertex angle is 18°.

One of the base angles is 4x + 9 so it is 4(18) + 9 or 81°