# PQRS is a parallelogram. m∠Q = 11x + 13 and m∠S = 15x - 23. Find the measure of ∠P.

PQRS is a parallelogram. $m\angle Q=11x+13$ and $m\angle S=15x-23$. Find the measure of $\angle P$.
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Cristiano Sears

A parallelogram has opposite angles that are congruent so:
$\angle Q\cong \angle S$
$m\angle Q=m\angle S$
$11x+13=15x-23$
$11x=15x-36$
$-4x=-36$
$x=9$
So, $m\angle Q=11\left(9\right)+13=112°.$
A parallelogram has consecutive angles that are supplementary:
$m\angle P+m\angle Q=180°$
$m\angle P+112°=180°$
$m\angle P=68°$

Jeffrey Jordon