Note that OL and ON form a 90° angle because they are perpendicular
This must mean that the sum of angles LOM and MON = 90° ........so.....
3x - 15 + 5x - 23 = 90 simplify
8x - 38 = 90 add 38 to both sides
8x = 128 divide both sides by 8
x = 16
So....MON = 5(16) - 23 = 80 - 23 = 57°