Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 4.9 AIME Find the answer Netherlands

In triangle ABC, a point $D$ lies on side $BC$ and a point $E$ lies on side $AC$ such that the line segments $BD$ , $DE$ , and $AE$ have the same length. The point $F$ is the intersection between the line segments $AD$ and $BE$ . Angle $C$ is $68^\circ$ .
What is the size of angle $F$ in triangle $AFB$ ?

A) $120^\circ$ B) $121^\circ$ C) $122^\circ$ D) $123^\circ$ E) $124^\circ$

This was a multiple-choice question, but the options didn't survive into the source we have. The answer given is E, and the solution below works it through.

Solution

E) $124^\circ$

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