Question

$PQRS$ is a parallelogram. From the information given in the figure, find the values of $x$ and $y$.

Answer 1

$PQRS$ is a parallelogram.

$PQ\parallel SR$ and $SQ$ is a transversal.

$\therefore$ $\angle RSQ=\angle PQS$ [ Alternate angles ]

$\Rightarrow$ ${48}^o=4x$

$\Rightarrow$ $x=\frac{{48}^o}{4}$

$\Rightarrow$ $x={12}^o$

$SP\parallel RQ$ and $SQ$ is transversal.

$\therefore$ $\angle PSQ=\angle RQS$ [ Alternate angles ]

$\Rightarrow$ ${63}^o=7y$

$\Rightarrow$ $y=\frac{{63}^o}{7}$

$\Rightarrow$ $y=9^o$

$\therefore$ The values of $x$ and $y$ are ${12}^o$ and $9^o.$