Chapter 4.6, Problem 51HP

To determine

To find: The measure of the vertex angle.

Answer to Problem 51HP

The measure of the vertex angle is $y=180°-2x$ .

Explanation of Solution

Given information: The given triangle is an isosceles triangle.

Calculation: As we know that the sum of all the angle of a triangle is $180°$ .

Now, let triangle $ABC$ be isosceles triangle.

  

Every isosceles triangle has one vertex angle two congruent angle.

Since $AB=AC$

Hence, $\angle BAC=\angle BCA$

Assume $x$ be the base angle and vertex angle will be y,

  $\begin{array}{l}x+x+y=180°\\ y=180°-2x\end{array}$