MathNet 2023-part-07 — 187 problems (EN–VI) Question 75

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