In an isosceles triangle KLM with base KM, the angle at the apex K is 50, LN is the median. Find the NLM angle.

Since the KLM triangle is isosceles with the base of the KM, then the angle LMB = LMK = 50.

The median LN, drawn to the base of the isosceles triangle KLM, also has the bisector and the height of the triangle.

Then the triangle MNL is rectangular with an angle MNL = 90.

The acute angles of a right triangle add up to 90.

Then the angle LM = (90 – LMN) = (90 – 50) = 40.

Answer: The angle of the LMM is 40.