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Find an angle sum in quadrilateral ABCD with AB=AD & CB=CD

Source: XV Rioplatense Mathematical Olympiad (2006), Level 3

August 10, 2011
geometryincentergeometry unsolved

Problem Statement

Let ABCDABCD be a convex quadrilateral with AB=ADAB = AD and CB=CDCB = CD. The bisector of ∠BDC\angle BDC intersects BCBC at LL, and ALAL intersects BDBD at MM, and it is known that BL=BMBL = BM. Determine the value of 2∠BAD+3∠BCD2\angle BAD + 3\angle BCD.
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