KöMaL 2017 B4877

Points $A$, $B$, $C$ and $D$, in this order, lie on a straight line. Point $E$ does not lie on the line, and $AEB\sphericalangle=BEC\sphericalangle =CED\sphericalangle = 45^\circ.$ Let $F$ and $G$ be the midpoints of $AC$ and $BD$, respectively. What is the measure of angle $FEG$?