MathNet 2023-part-01 — 191 problems (EN–VI) Question 12

Let $ABCD$ be a convex quadrilateral such that $AB = CD$, $\angle BCD = 2\angle BAD$, $\angle ABC = 2\angle ADC$, and $\angle BAD \neq \angle ADC$. Find the angle between diagonals $AC$ and $BD$.