, 2021

Join $S$ to $T$ and $R$ to $T$. [[IMAGE0]] Since $PQRS$ is a square, $\angle SPQ = 90^\circ$. Since $\triangle PTQ$ is equilateral, $\angle TPQ = 60^\circ$. Therefore, $\angle SPT = \angle SPQ + \angle TPQ = 90^\circ + 60^\circ$. Since $PQRS$ is a square, $SP= PQ$. Since $\triangle PTQ$ is equilateral, $TP = PQ$. Since $SP = PQ$ and $TP = PQ$, then $SP = TP$ which means that $\triangle SPT$ is isosceles. Thus, $\angle PTS = \frac{1}{2}(180^\circ - \angle SPT) = \frac{1}{2}(180^\circ - 150^\circ) = 15^\circ$. Using a similar argument, we can show that $\angle QTR = 15^\circ$. This means that $\angle STR = \angle PTQ - \angle PTS - \angle QTR = 60^\circ - 15^\circ - 15^\circ = 30^\circ$.