Let triangles $STU$ and $OPQ$ be right isosceles triangles on the $xy$-plane. $STU$ has vertices $S=(3,2)$, $T=(3,8)$, $U=(9,2)$. $OPQ$ has vertices $O=(3,2)$, $P=(3,8+t)$, $Q=(9+t,2)$. If the measure of $\angle T$ is $a^{\circ }$, what is the measure of $\angle Q$?