We know that KLMN is a parallelogram
Parallelograms have the following properties (to highlight a few):
I. Opposite sides are congruent (same) i.e. KN = LMN
II. Opposite angles are congruent (same) i.e. K = M & L = N
III. Consecutive angles are supplementary (they add up to 180 degrees) i.e. N + K = 180 degrees & L + M = 180 degrees
Therefore, N & K are supplementary angles