# 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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