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Find the value of angle KNL

Source: Tournament of Towns Spring 2003 - Junior O-Level - Problem 3

June 14, 2011
geometrytrapezoidgeometry proposed

Problem Statement

Points KK and LL are chosen on the sides ABAB and BCBC of the isosceles △ABC\triangle ABC (AB=BCAB = BC) so that AK+LC=KLAK +LC = KL. A line parallel to BCBC is drawn through midpoint MM of the segment KLKL, intersecting side ACAC at point NN. Find the value of ∠KNL\angle KNL.
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