Chapter 6.2, Problem 19PPS

To determine

The value of each variable in each parallelogram.

Answer to Problem 19PPS

  $x=58,y=63.5$

Explanation of Solution

Given:

The given figure is:

Calculation:

The consecutive angles of a parallelogram are supplementary.

Therefore, angles G and H are consecutive angles and supplementary.

So,

  $\begin{array}{l}m\angle G+m\angle H=180\\ \left(x-5\right)+\left(2x+11\right)=180\\ 3x+6=180\\ 3x=174\\ x=58\end{array}$

Also, the opposite angles of a parallelogram are congruent. Angles F and H are opposite angles, hence, are congruent.

  $\begin{array}{l}m\angle F=m\angle H\\ 2y=2x+11\\ 2y=2\left(58\right)+11\\ 2y=127\\ y=63.5\end{array}$