MathNet 2025 — 50 problems — Part 01 Question 48

Let $ABCD$ be a trapezoid such that $AB \parallel CD$, $AD = 13$, $BC = 15$, $AB = 20$, and $CD = 34$. Point $X$ lies inside the trapezoid such that $\angle XAB = 2\angle XBA$ and $\angle XDC = 2\angle XCD$. Compute $XD - XA$.