Triangles $ABC$ and $DEF$ are graphed in the $xy$-plane. Triangle $ABC$ has vertices $A,B,$ and $C$ at $(2,3)$, $(2,7)$, and $(6,3)$, respectively. Triangle $DEF$ has vertices $D,E,$ and $F$ at $(2,3)$, $(2,7+m)$, and $(6+m,3)$, respectively, where $m$ is a positive constant. If the measure of $\angle B$ is $x^{\circ }$, what is the measure of $\angle F$?