What is the measure of the angle CGF in the given figure?

Question

What I could gather: $$CX=CY=CE=CF=r$$ $$\measuredangle CEB=\measuredangle CFD=90^{\circ}.$$ $$\measuredangle XCE=65^{\circ}$$ $$\measuredangle CEF= \measuredangle CFE$$

Please help me solve this. Thank you.

Answer 1

Since $\measuredangle ECF=90^{\circ}$, $CE=CF$ and $\Delta BCE\cong\Delta DCF$, we obtain: $$\measuredangle CGF=45^{\circ}+25^{\circ}=70^{\circ}.$$

Answer 2

You are almost there. Note that $\measuredangle GCF$ is also $65^\circ$, and $\angle ECF$ is right. But $\triangle ECF$ is isosceles, so what is $\measuredangle CFG$?