We know that if a transversal line intersects two given lines in such a way that the sum of the measures of the angles on the same side of transversal is 180^o, then the given two lines are parallel to each other.

Hence,

∠NML + ∠MLK = 180°

Hence, NM||LK

As quadrilateral KLMN has a pair of parallel lines, therefore, it is a trapezium