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° )
correct.
