$ABC$ is a right angled triangle at $B$.On side $AB$ points $E$ and $F$ are taken such that $AE=EF=FB=BC$.Let, $\angle CAE=x^0$,$\angle CEF=y^0$ and $\angle CFB=z^0$. Now,prove that $x^0+y^0=z^0$.
I can do it using inverse trig functions and finding the angles.But I would like a more geometrical proof.
Any help is highly appreciated.
Draw a picture like this. Observe that the indicated angles are equal to $x$ and $y$ and that triangle $XYZ$ is right-angled and isosceles.