The measure of the angle LMN is 90O.
Note that you can draw a 90° angle at either end of line segment AB if you want to (in other words at point A or point B). Simply extend AB beyond A or beyond B, and then follow the above steps. Point A (or point B) would serve as point O in the above instructions. This is essentially the same method featured in How to Construct a Perpendicular Line to a Given Line Through Point on the Line, Method 2.