In the diagram below, PQ is a diameter of the circle. Find angle XYZ in degrees.
Angle XYZ is (180 - 80 - 35) + 80/2 = 105 degrees.
I figured out the answer, but i'll post it in case anybody wants to read it.
We see that arc XZ is 180-80-35=65, so angle XYZ=(180+65)/2=122.5
It's interesting that the sum of the internal angles of the shape OXYZ is equal to the angle XYZ.
17.5° +65° + 40° = 122.5°