Chapter 15, Problem 10CR

To determine

To Find: The measurement of the vertex angle.

Answer to Problem 10CR

  ${36}^o$

Explanation of Solution

Given:

  $\begin{array}{l}\text{In Isosceles triangle }\\ \text{Base Angle}=2\text{ Vertex angle}\end{array}$

Formula Used:

Base-Angle Theorem: It states that the side opposite to the congruent angle of a triangle are congruent.

Calculation:

  $\begin{array}{l}\text{In Isosceles triangle }\\ \text{Base Angle}=2\text{ Vertex angle}\\ Let,\\ \text{Vertex angle be}x\\ then,\\ 2x+2x+x=180\left(\text{sum of angle of triangle}\right)\\ \text{⇒}5x=180\\ \text{⇒}x=\frac{180}{5}\\ \text{⇒}x={36}^o\end{array}$

Conclusion:

Thus the required angle is ${36}^o$ .