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Easy looking geometry not very easy to solve

Source: Belarus TST 2024

July 17, 2024
geometry

Problem Statement

An isosceles triangle ABCABC is given(AB=BCAB=BC). Point DD lies inside of it such that ∠ADC=150\angle ADC=150, EE lies on CDCD such that AE=ABAE=AB. It turned out that ∠EBC+∠BAE=60\angle EBC+\angle BAE=60. Prove that ∠BDC+∠CAE=90\angle BDC+\angle CAE=90 D. Vasilyev
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