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equal angles in a right triangle, danube junior geometry 2012

Source: Danube 2012 Junior P3

September 6, 2018
geometryequal angles

Problem Statement

Let ABCABC be a triangle with ∠BAC=90o\angle BAC = 90^o. Angle bisector of the ∠CBA\angle CBA intersects the segment (AB)(AB) at point EE. If there exists D∈(CE)D \in (CE) so that ∠DAC=∠BDE=xo\angle DAC = \angle BDE =x^o , calculate xx.
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