If we look at the angle KLQ, we see it sits on a straight line along with a right angle. So this angle is determined by subtracting MLN and 90 from 180 (angles on a straight line)

In triangle MLN, the angle LMN is determined in exactly the same way (this time since all angles in a triangle sum to 180), therefor KLQ and LMN are the same. Since both triangles also have a right angle in them, it follows that the third angle in each is the same

All angles the same => similar