Triangles $RST$ and $UVW$ are graphed in the $xy$-plane. Triangle $RST$ has vertices $R,S,$ and $T$ at $(2,3),(2,8),$ and $(7,3),$ respectively. Triangle $UVW$ has vertices $U,V,$ and $W$ at $(2,3),(2,3+5k),$ and $(2+5k,3),$ respectively, where $k$ is a positive constant. If the measure of $\angle T$ is $p^{\circ },$ what is the measure of $\angle W$?