Question

Find the measure of $\angle P$, if $\overline{SP}||\overline{RQ}$ in the given figure.

Answer 1

$PQRS$ is a qudrilateral with $PS\parallel QR$ and $\angle Q={130}^o$

$\therefore PQRS$ is a trapezium

So $\angle Q\&\angle P$ are adjacent angles within the parallel sides $PS\&QR$

Now the sum of the adjacent angles within the parallel sides of a trapezium is ${180}^o$

$\therefore \angle Q+\angle P={180}^o⟹\angle P={180}^o-\angle Q$

But $\angle Q={120}^o$ ...... (given)

$\therefore \angle P={180}^o-{130}^o={50}^o.$

$⟹\angle P={50}^o.......\left(i\right)$

By the similar reason,

$\angle S+\angle R={180}^o⟹\angle S={180}^o-\angle R$

But $\angle R={90}^o$ ....... (given)

$\therefore \angle S={180}^o-{90}^o={90}^o.$

$⟹\angle S={90}^o.......\left(ii\right)$

$\angle P={50}^o,\angle S={90}^o.$