Question

$overrightarrow{qs}$ bisects $angle pqr$ and $mangle pqs = 63^{circ}$.

Explanation:

Step1: Recall angle - bisector property

An angle - bisector divides an angle into two equal parts. So if $\overrightarrow{QS}$ bisects $\angle PQR$, then $\angle PQS=\angle SQR$.

Step2: Find the measure of $\angle PQR$

Since $\angle PQR=\angle PQS + \angle SQR$ and $\angle PQS=\angle SQR = 63^{\circ}$, then $\angle PQR=63^{\circ}+63^{\circ}$.
$\angle PQR = 126^{\circ}$

Answer:

$126^{\circ}$