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JK = MN because of Given

∠JLK = ∠MLN because of the vertical angle theorem

JL = LN because of definition of midpoint

ΔJLK = MLN because of SAS

∠K = ∠N because corresponding angles of congruent triangles are congruent.

Hope this helps!
check the picture below.

so, therefore, the triangles KLJ and NLM have a side, then another adjacent side and an angle in common, Side Side Angle.  That means both triangles are congruent, and if they're congruent, so are all of their angles too.
Ver imagen jdoe0001

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