since LON is a straight angle, it equals 180 degrees. That makes LOM and MON supplementary angles. Thus, we know (7x-92) + (6x+12) = 180. Since both are positive, we can drop the parentheses.
7x - 92 + 6x + 12 = 180
Simplify: 13x - 80 = 180
Add 80 to both sides: 13x = 260
Divide both sides by 13: x = 20
Plug in: 7(20)-92
140 - 92
LOM is 48 degrees.