If you construct a line from Point B horizontally to intersect DC at right angles at Point E, from symmetry you can see that the length of that line is R sin(64). And from that the angle BDC (which also equals angle x) is arctan(Rsin(64)/(R+Rcos(64)). From that you have angle x.

Length CE is then R-Rcos(64), so angle y is arctan(Rsin(64)/(R-Rcos(64)).