VTMO 2026 - Grade 7 - Semifinal - SET 3 - Self-study Question 14

In triangle $ABC$, $\angle B=40^\circ$ and $\angle C=80^\circ$. A line parallel to $AB$ meets $CA$ and $CB$ at $M$ and $N$, respectively, such that $AM=MN$. Find $\angle BAN$ in degrees.