Langley’s Adventitious Angles

Geometry Level 2

\(ABC\) is an isosceles triangle.
\(B = C = 80 ^\circ\).
\(CF\) at \(30^\circ\) to \(AC\) cuts \(AB\) in \(F.\) \(BE\) at \(20^\circ\) to \(AB\) cuts \(AC\) in \(E\).

Find then angle \(BEF \) in degrees.

One of the all-time most famous geometry problems! Will wreck your brains if you haven't done this earlier, surely!

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