Triangle $ABC$ has vertices $A(1,1)$, $B(1,1+m)$, and $C(1+m,1)$, where $m$ is a positive constant. Triangle $DEF$ has vertices $D(1,1)$, $E(1,1+2m)$, and $F(1+2m,1)$. If the measure of $\angle B$ is $x^{\circ }$, what is the measure of $\angle F$?