DF−→− bisects ∠EDG. Find FG. The diagram is not to scale.
Since $\overleftrightarrow{DF}$ bisects $\angle EDG$, we have \begin{align*}
\angle EDF &= \angle FDG \\
4x &= 5x + 20.
\end{align*}Thus, $x = -20$. Therefore, \begin{align*}
FG &= 5x - 5(-20)\\
&= 5x + 100 \\
&= 5(-20) + 100 \\
&= -100 + 100\\
&=\boxed{0}.
\end{align*}