HMMT November 2021 H1

Let $n$ be the answer to this problem. In acute triangle $A B C$, point $D$ is located on side $B C$ so that $\angle B A D=\angle D A C$ and point $E$ is located on $A C$ so that $B E \perp A C$. Segments $B E$ and $A D$ intersect at $X$ such that $\angle B X D=n^{\circ}$. Given that $\angle X B A=16^{\circ}$, find the measure of $\angle B C A$.