Chapter 9, Problem 3SAP

To determine

To find: correct option that represents the value of $x$ .

Answer to Problem 3SAP

E.

Explanation of Solution

Given information:

The figure is shown below.

  

In the given figure, $PQRS$ is a parallelogram and $\overline{MN}$ is a line segment.

The options are as follows:

  $180-b$

  $180-c$

  $a+b$

  $a+c$

  $b+c$

Calculation:

Label the figure as shown below.

  

The value of $x$ can be evaluated as follows:

  $\begin{array}{c}y=\angle SRE+\angle MEQ\left[\text{Exterior angle property}\right]\\ y=b+c\left[\begin{array}{l}\angle SRE=b;\text{ Corresponding angles}\\ \angle MEQ=c;\text{ Alternate angles}\end{array}\right]\\ x=b+c\left[x=y;\text{ Alternate angles}\right]\end{array}$

Thus, option E. is correct.