Answers:
x = 19
angle M = 68 degrees
Step-by-step explanation
Vertical angles are always congruent.
angle M = angle O
4x-8 = 3x+11
4x-3x = 11+8
x = 19
Use this value of x to find angle M.
angle M = 4x-8 = 4*19-8 = 68 degrees
As a check, let's find angle O as well.
angle O = 3x+11 = 3*19+11 = 68
The answers are confirmed.