Let $AB$ be the diameter of a semicircle. $C$, $D$, and $E$ are points on $AB$, in that order, such that $AC=1$, $CD=3$, $DE=4$, and $EB=2$. From $C$ and $E$, draw perpendicular lines of $AB$, intersecting the semicircle at $F$ and $G$, respectively. Find the measurement of $\angle{FDG}$.