Chapter 8.1, Problem 65SPR

To determine

The value of x and y.

Answer to Problem 65SPR

  $x=34$

  $y=\pm 5$

Explanation of Solution

Given:

The given figure is:

  

Calculation:

The figure can be drawn as:

  

According to the Corresponding angles postulate,

  $\begin{array}{l}2x=68\\ x=\frac{68}{2}\\ x=34\end{array}$

According to the Triangle angle sum theorem,

  $\begin{array}{l}68+\left(3x-15\right)+y^2=180\\ 68+\left(3\left(34\right)-15\right)+y^2=180\\ 155+y^2=180\\ y^2=25\\ y=\pm 5\end{array}$