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Solve for the angle

Source: Lusophon Mathematical Olympiad 2023 Problem 2

May 27, 2023
geometry

Problem Statement

Let DD be a point on the inside of triangle ABCABC such that AD=CDAD=CD, ∠DAB=70∘\angle DAB=70^{\circ}, ∠DBA=30∘\angle DBA=30^{\circ} and ∠DBC=20∘\angle DBC=20^{\circ}. Find the measure of angle ∠DCB\angle DCB.
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