the vertex angle of an isosceles triangle measures 36 degrees . what is the measure of its base angle?

Explanation:

For any triangle, the three angles always add to 180 degrees.

In an isosceles triangle, the base angles are the same measure. For now we don't know what they are, so let's call them x. The vertex angle is 36.

Adding the three angles (x,x, and 36) and setting that equal to 180 will help us find the value of x.

x+x+36 = 180

2x+36 = 180

2x+36-36 = 180-36 subtract 36 from both sides

2x = 144

2x/2 = 144/2 divide both sides by 2

x = 72

This triangle has two base angles of 72 each and the vertex angle of 36. As a check, the three angles should add up to 180

72+72+36 = 144+36 = 180

So the answer is confirmed.