Distance Around a Parallelogram

Geometry Level 5

\(ABCD\) is a parallelogram. \(E \) is a point on \(DC\) extended, such that \(D\) and \(E\) are on opposite sides of \(BC\). Let \(AE\) intersect \(BC\) and \(BD\) at \(F\) and \(G\), respectively. If \(AG = 180\) and \(FG = 108\), what is \(EF\)?

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