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Find measure of angle

Source: Romanian District Olympiad 2014, Grade 7, P3

June 15, 2014
trigonometrygeometryincenterangle bisectorsimilar trianglesgeometry proposed

Problem Statement

Let ABCABC be a triangle in which ∡A=135∘\measuredangle{A}=135^{\circ}. The perpendicular to the line ABAB erected at AA intersects the side BCBC at DD, and the angle bisector of ∠B\angle B intersects the side ACAC at EE. Find the measure of ∡BED\measuredangle{BED}.
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