LKN = 90 degrees
Let's solve this with a different approach:
LM = 3, KN = 13 --> Given
HN = (KN + LM) / 2 = (13+3)/2 = 16/2 = 8
LN =
--> Given
=
--> Pythagorean Theorem
We get: LH = 5
Similarly,
KH = (KN - LM) / 2 = (13-3)/2 = 10/2 = 5
We now see that triangle LHK is isosceles - both sides are equal
KHL = 90 degrees --> Def. of altitude
That leaves angle HLK = angle LKN = 90/2 = 45 degrees --> Base angle theorem.
LKN = 90 degrees