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 $8,10,118°$and $62°$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 given figure, $\overline{PS}\cong \overline{QR}$implies that $a=8$and $\overline{PQ}\cong \overline{SR}$implies that $b=10$.

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 $\angle y\cong \angle PSR$implies that

$\begin{array}{c}y=m\angle PSR\\ =62°\end{array}$

Step 5. Description of step.

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

$\begin{array}{c}m\angle PSR+m\angle SRQ=180\\ 62+x=180\\ x=180-62\\ =118°\end{array}$

Therefore, the values of a, b, x and y are $8,10,118°$and$62°$ respectively.