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pairs of equal angles in a convex pentagon wanted

Source: Ukrainian TST 1999 p5

February 13, 2020
pentagonequal anglesgeometry

Problem Statement

A convex pentagon ABCDEABCDE with DC=DEDC = DE and ∠DCB=∠DEA=90o\angle DCB = \angle DEA = 90^o is given. Let FF be a point on the segment ABAB such that AF:BF=AE:BCAF : BF = AE : BC. Prove that ∠FCE=∠ADE\angle FCE = \angle ADE and ∠FEC=∠BDC\angle FEC = \angle BDC.
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