Chapter 12.4, Problem 14E

To determine

To Find: The value of $xandy.$

Answer to Problem 14E

  $x={20}^{°},y={70}^{°}$

Explanation of Solution

Given:

  

The vertex angle of the isosceles triangle is supplementary to ${40}^{°}$

i.e.

  $180-{40}^{°}={140}^{°}$

Now using the angle sum property.

  $\begin{array}{l}{x}^{°}+x^{°}+{140}^{°}={180}^{°}\\ 2x+140=180\\ 2x=40\\ x={20}^{°}\end{array}$

Now

We know that the acute angles of the right triangle are complementary.

Thus

  $\begin{array}{l}{x}^{°}+y^{°}={90}^{°}\\ 20+y=90\\ y=90-20\\ y={70}^{°}\end{array}$

Hence, $x={20}^{°},y={70}^{°}$