jmc

If the measure of $\angle TSQ$ is $145^{\circ }$, then the measure of $\angle TSP$ is $180^{\circ }-145^{\circ }=35^{\circ }$ since they are supplementary angles. The measure of $\angle RQP$ is also $35^{\circ }$ since sides $TS$ and $RQ$ are parallel. Now we have two of the three angles in triangle $PQR$. To find the third, we calculate $180^{\circ }-65^{\circ }-35^{\circ }=80^{\circ }$. The measure of $\angle PRQ$ is $\boxed{80^{\circ }}$.