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Geometry with fixed angles

Source: Bulgaria JBMO TST 2017 P1 Day 1

August 26, 2019
geometrygeometry proposed

Problem Statement

Given is a triangle ABCABC and let AA1AA_1, BB1BB_1 be angle bisectors. It turned out that ∠AA1B=24∘\angle AA_1B=24^{\circ} and ∠BB1A=18∘\angle BB_1A=18^{\circ}. Find the ratio ∠BAC:∠ACB:∠ABC\angle BAC:\angle ACB:\angle ABC.
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