MathNet 2023-part-07 — 187 problems (EN–VI) Question 126

Suppose $ABCD$ is a convex quadrilateral with $\angle ABD = 105^{\circ}$, $\angle ADB = 15^{\circ}$, $AC = 7$, and $BC = CD = 5$. Compute the sum of all possible values of $BD$.