In the figure, PQ = PS and SRP is a straight line. Find $\angle\text{RQS}$. Ans: ___ $^\circ$

1. Find the base angles of the isosceles triangle PQS

Since $PQ = PS$, $\triangle PQS$ is an isosceles triangle.
$\angle PQS = \angle PSQ = \frac{180^\circ - \angle QPS}{2}$
$\angle PQS = \frac{180^\circ - 27^\circ}{2} = \frac{153^\circ}{2} = 76.5^\circ$

2. Find angle RQS

$\angle RQS = \angle PQS - \angle PQR$
$\angle RQS = 76.5^\circ - 44^\circ = 32.5^\circ$