$\left[\begin{array}{l}\text { Symmetry helps solve the problem } \\ \text { [The inscribed angle is half the central angle]}\end{array}\right]$

$A B$ is the diameter of the circle; $C, D, E$ are points on the same semicircle $A C D E B$. On the diameter $A B$, points $F$ and $G$ are taken such that $\angle C F A = \angle D F B$ and $\angle D G A = \angle E G B$. Find $\angle F D G$, if the arc $A C$ is $60^{\circ}$ and the arc $B E$ is $20^{\circ}$.