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Find angle measure in convex quadrilateral

Source: Turkey IMO TST 1995 #4

July 8, 2011
geometryperpendicular bisectorangle bisectorgeometry unsolved

Problem Statement

In a convex quadrilateral ABCDABCD it is given that ∠CAB=40∘,∠CAD=30∘,∠DBA=75∘\angle{CAB} = 40^{\circ}, \angle{CAD} = 30^{\circ}, \angle{DBA} = 75^{\circ}, and ∠DBC=25∘\angle{DBC}=25^{\circ}. Find ∠BDC\angle{BDC}.
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