Question

PQRS is a parallelogram. Find the values of a, b, x and y.

Short answer

The values of a, b, x and y are$8,15,80°$ and $70°$respectively.

Step-by-step solution

Step 1. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

Step 2. Description of step.

In the given figure, $\overline{PS}\cong \overline{QR}$implies that $a=8$and $\overline{PQ}\cong \overline{SR}$implies that$b=15$.

Step 3. Apply property of parallelogram.

The opposite angles of a parallelogram are congruent.

Step 4. Description of step.

From the given figure, it can be observed that $\angle x\cong \angle QPS$implies that

$\begin{array}{c}x=m\angle QPS\\ =80°\end{array}$

Step 5. Description of step.

Both pairs of opposite sides of a parallelogram are parallel, that is, $\overline{PS}\left|\right|\overline{QR}$and $\overline{SQ}$is a transversal then same side interior angles are supplementary.

$\begin{array}{c}m\angle PQR+m\angle QRS=180\\ 30+y+80=180\\ y=180-110\\ =70°\end{array}$

Therefore, the values of a, b, x and y are $8,15,80°$and $70°$respectively.