Chapter 7.1, Problem 10PSA

To determine

To find:The measure of the vertex angle of the given triangle

Answer to Problem 10PSA

The measure of the vertex angle is ${45}^0$

Explanation of Solution

Given information:The following statement has been given

The vertex of an isosceles triangle is twice as large as one of the base angles

Formula used:The base angles of an isosceles triangle are congruent

Calculation:We know that base angles of an isosceles triangle are congruent

Thus, is vertex angle being twice as large as one of the base angles, then it is twice as large as both of the base angles. Hence, we can say that

  $x=2y$ , and

  $x+y+y={180}^0$

Where x is the vertex angle and yis the base angle.

Hence, on solving the two equations, we get

  $x={45}^0$