In the diagram below, line MN is a diameter of the circle. Find angle XYZ, in degrees.

Diagram: https://latex.artofproblemsolving.com/b/5/c/b5ca879e6891c11d8a31ce8210b4763a6e773423.png

tysm <3

Note that

Angle M = (1/2) its intercepted arc = (1/2)(80) = 40°

Similarly, angle N = (1/2) 35 = 17.5°

Then in triangle MYN angle MYN =180 - 40 - 17.5 = 122.5°

But angle XYZ is a vertical angle to angle MYN so it also measures 122.5°

CPhill is (this time)correct.

Line WO bisects angle MOX and it's parallel to XY

Line VO bisects angle NOZ and it's parallel to YZ

∠WOV = ∠XYZ = 180° - ( 40° + 17.5° )