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MathNet 2021 — Part 04 Question 23

Math Olympiad Vault · MathNet 2021 — Part 04

Question 23

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 $\angle B C A$.