If OL is perpendicular to NO, then where they meet is a right angle. 90°. That means that ∠LOM and ∠MON add up to equal 90°. Use the values they gave us to do this: 3x+38°+9x+28°=90°. 12x + 66 = 90. 12x = 24 and x = 2. ∠LOM= 3x + 38° so ∠LOM = 3(2) + 38, which is 44. There you go!