In $\Delta PQR$, $S$ and $T$ are points on the sides $PQ$ and $PR$, respectively, such that $\Delta PST$ is similar to $\Delta PRQ$. If $\text{m}\angle PQR=47^{\circ }$, then find $\text{m}\angle STR$.

Given that $\Delta PST\sim \Delta PRQ$.By the property of similar triangles, corresponding angles are equal:
$$\angle PST=\angle PRQ$$
$$\angle PTS=\angle PQR$$
We are given that $\text{m}\angle PQR=47^{\circ }$. Therefore:
$$\angle PTS=47^{\circ }$$
Since $S$ and $T$ lie on the sides $PQ$ and $PR$ respectively, $PTR$ forms a straight line. The angles $\angle PTS$ and $\angle STR$ are supplementary (linear pair):
$$\angle PTS+\angle STR=180^{\circ }$$
$$47^{\circ }+\angle STR=180^{\circ }$$
$$\angle STR=180^{\circ }-47^{\circ }=133^{\circ }$$