VTMO 2026 - Grade 8 - Semifinal - SET 3 - Self-study Question 1

Triangle $ABC$ is isosceles with $AB=AC$. Equilateral triangle $DEF$ lies inside it, with $D,E,F$ on $AB,BC,AC$, respectively, as shown. Given $\angle ADF=50^\circ$ and $\angle A=\tfrac12\angle DEF$, find $\angle BED$.