Question

The measure of the vertex angle of an isosceles triangle is (a + 30)°. The base angles each measure (2a - 15)º. What is the measure in degrees of one of the base angles?​

Answer 1

To be able to fine one of the bases we must first find the vertex and to do that we have to find the value of a.

A triangle measures 180 degrees.
Therefore we must form an equation that is equal to 180 degrees.


(a + 30) + 2(2a - 15) = 180

We put 2 in front of (2a - 15) because there are two base angles.

Solution:

(a + 30) + 2(2a - 15) = 180
a + 30 + 4a - 30 = 180
a + 4a + 30 - 30 = 180
5a = 180
5a/5 = 190/5
a = 36 degrees

Therefore the base = 2(36) - 15 = 57 deg