Question

Find the measure of $∠P$ and $∠S$ if $\bar {SP} || \bar{RQ}$ in Figure. (If you find $m∠R$, is there more than one method to find $m∠P$ ?)

Answer 1

$\Rightarrow$ $∠ P + ∠ Q = 180°$ (Angles on the same side of transversal)
$\Rightarrow$ $∠ P + 130° = 180°$
$\Rightarrow$ $∠ P = 50°$
$\Rightarrow$ $∠ R + ∠ S = 180°$ (Angles on the same side of transversal)
$\Rightarrow$ $90° + ∠ R = 180°$
$\Rightarrow$ $∠ S = 90°$
Yes. There is one more method to find the measure of $m∠ P$.
$m∠ R$ and $m∠ Q$ are given.
After finding $m∠ S$, the angle sum property of a quadrilateral can be applied to find $m∠ P$.