MathDB
hidden triple angle???(2023 HMMT G6)

Source:

February 21, 2023

Problem Statement

Convex quadrilateral ABCDABCD satisfies CAB=ADB=30,ABD=77,BC=CD\angle{CAB} = \angle{ADB} = 30^{\circ}, \angle{ABD} = 77^{\circ}, BC = CD and BCD=n\angle{BCD} =n^{\circ} for some positive integer nn. Compute nn.