Chapter 12.4, Problem 33E

To determine

To Explain: Why the measure of the vertex angle of an isosceles triangle must be an even number of degrees when the measure of all the triangles are whole numbers.

Answer to Problem 33E

  $\frac{180-x}{2}$

Explanation of Solution

Given: Isosceles triangle.

The vertex angle of the isosceles triangle must be even number because

The base angles of the triangle are congruent.

Let the vertex angle be $x$ .

Then

Measure of each angle

  $\frac{180-x}{2}$

Which will be a whole number only if $x$ is even.