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Ingle inequality in an inscribed pentagon

Source: Sharygin Geometry Olympiad Correspondence round 2016 P-8 Grade 8-9

February 20, 2017
inequalitiesgeometry

Problem Statement

Let ABCDEABCDE be an inscribed pentagon such that ∠B+∠E=∠C+∠D\angle B +\angle E = \angle C +\angle D.Prove that ∠CAD<π/3<∠A\angle CAD < \pi/3 < \angle A.
(Proposed by B.Frenkin)
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