Problem

Source:

Tags: geometry



A duck drew a square $ABCD$, then he reflected $C$ across $B$ to obtain a point $E$. He also drew the center of the square to be $F$. Then, he drew a point $G$ on ray $EF$ beyond $F$ such that $\angle AGC = 135^{\circ}$. Help the Duck prove that $\angle CGD = 135^{\circ}$ as well.