A, B and C are points on the circle where O is the center. 

Find the angles X, Y and Z

X = Y + 52.5

X = 

You know triangle OCB is isosceles since two of its sides are radii, so base angles Z and <OCB have to be congruent and have to add to 180 - 35 so do that and divide by 2

And for similar reasons <OCA is 52.5; add that to <OCB and subtract from 180 (since those two angles plus x make a line) to get x