The measure of the vertex angle of an isoceles triangle is one- fourth that of a base anglemeasure of each base angle? measure of vertex angle?

Base angle = 72

Vertex angle = 18

Step-by-step explanation:

Measure of the base angle = x. But there are two of them. (Definition of isosceles).  Keep that in mind.

The vertex angle is 1/4 of one of the base angles. That means that the vertex is 1/4 x

All three angles = 180 degrees.

So we have x + x + x/4 = 180 degrees.

change 1/4x to 0.25x x since 1/4 = 0.25

Equation

x + x + 0.25 = 180

2.5x  = 180

Solution

2.5x = 180                      Divide by 2.5 on both sides

2.5x/2.5 = 180/2.5

x = 72

Answer

That means that each base angle = 72 degrees

The Vertex Angle = 72/4 = 18