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equal angles with an interior point of a parallelogram, easy danube geometry

Source: Danube 2011 P1

September 8, 2018
geometryparallelogramequal anglesquadrilateral

Problem Statement

Let ABCMABCM be a quadrilateral and DD be an interior point such that ABCDABCD is a parallelogram. It is known that ∠AMB=∠CMD\angle AMB =\angle CMD. Prove that ∠MAD=∠MCD\angle MAD =\angle MCD.
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