circle arc proof 
I have this picture and I have to show angle phi is equal to angle theta and I can assume both circles are the same. I'm having trouble getting started.I know that there are congruent line segments but that doesn't mean the arcs are of the same measure too or does it. Basically arcs CD and WZ for example?

If you know the theorem about Interior angles to circle , then check the following hints:
1) In a circle, cords with the same length intercept equal arcs  and thus , for example $\,\widehat{AB}=\widehat{XY}\,$
2) An interior angle equals the semisum of the two arcs its legs intercept, so for example
$$\phi=\frac{1}{2}\left(\widehat{AB}+\widehat{CD}\right)$$
Now prove your stuff.
