Question

which of the following statements are true if this door slides 2 feet to the right ? Select two that apply .

Answer 1

If the door slides 2 feet the door is moved the same distance and in the same direction so the door doen't chage the size or shape. Then, in order to answer the question, we need to find the measure of the angles P and R. Since the figure shows a parallelogram then angle P and R are congruent. This means that

$\angle P=\angle R$

or equivalently,

$12x+8=10x+16$

So by subtracting 10x to both sides, we have

$2x+8=16$

and by subtracting 8 to both sides, we get

$2x=8$

Then x is given by

$x=\frac{8}{2}=4$

Then, the measure of angles P ang R are

$\begin{gathered} \angle P=\angle R=12(4)+8 \\ \angle P=\angle R=56 \end{gathered}$

We also know that consecutive angles are supplementary, this means that

$\begin{gathered} \angle S+\angle R=180 \\ \text{and} \\ \angle P+\angle Q=180 \end{gathered}$

Therefore, we have that

$\begin{gathered} \angle S=\angle Q=180-56 \\ \angle S=\angle Q=124 \end{gathered}$

Finally, since segment PQ and SR are parallel and PS and QR are parallel each other, the answers are:

$\begin{gathered} \text{ Side PQ would be parallel to side SR and angle R would measure 56} \\ \\ \text{ Side PS would be parallel to side QR and angle S would measure }124 \end{gathered}$

which correspond to the first and second options from top to bottom.