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Convex pentagon with 3 equal sides

Source: IGO 2022 Elementary P3

December 14, 2022
pentagoniranian geometry olympiadgeometry

Problem Statement

Let ABCDEABCDE be a convex pentagon such that AB=BC=CDAB = BC = CD and ∠BDE=∠EAC=30∘\angle BDE = \angle EAC = 30 ^{\circ}. Find the possible values of ∠BEC\angle BEC.
Proposed by Josef Tkadlec (Czech Republic)
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