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ASU 159 All Soviet Union MO 1972 rectangle <QNM=<MNP wanted

Source:

July 3, 2019
geometryrectangleequal angles

Problem Statement

Given a rectangle ABCDABCD, points MM -- the midpoint of [AD][AD] side, NN -- the midpoint of [BC][BC] side. Let us take a point PP on the extension of the [DC][DC] segment over the point DD. Let us denote the intersection point of lines (PM)(PM) and (AC)(AC) as QQ. Prove that the ∠QNM=∠MNP\angle QNM= \angle MNP
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