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

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:

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°