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A tough find of angles in a quadrilateral

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October 22, 2010
geometryangle bisectorgeometry unsolved

Problem Statement

In a quadrilateral ABCDABCD, we have ∠DAB=110∘,∠ABC=50∘\angle DAB = 110^{\circ} , \angle ABC = 50^{\circ} and ∠BCD=70∘\angle BCD = 70^{\circ} . Let M,N M, N be the mid-points of ABAB and CDCD respectively. Suppose PP is a point on the segment MNM N such that AMCN=MPPN\frac{AM}{CN} = \frac{MP}{PN} and AP=CPAP = CP . Find ∠APC\angle AP C.
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