Chapter 7.2, Problem 36PPS

To determine

To find: The value of the variable.

Answer to Problem 36PPS

The value of x is 21 and the value of y is 65.

Explanation of Solution

Given:

  

Calculation:

It is given that $\Delta JKL\sim \Delta WYZ$

Now, from the property of similar triangle.

  $\begin{array}{l}m\angle J=m\angle W\\ 4x-13=71\\ x=21\end{array}$

Use the triangle angle-sum theorem,

  $\begin{array}{l}m\angle W+m\angle Y+m\angle Z=180\\ 71+m\angle Y+44=180\\ m\angle Y=65\end{array}$

So,

  $\begin{array}{c}y=m\angle Y\\ =65\end{array}$

Thus, the value of x is 21 and the value of y is 65.