Geometry Level 5

Trapezoid $$ABCD$$ has right angles at $$C$$ and $$D$$, and $$AD$$ > $$BC$$. Let $$E$$ and $$F$$ be the points on $$AD$$ and $$AB$$, respectively, such that $$\angle BED$$ and $$\angle DFA$$ are right angles. Let $$G$$ be the point of intersection of segments $$BE$$ and $$DF$$. If $$\angle CED = 58^{\circ}$$ and $$\angle FDE = 41^{\circ}$$, what is $$m\angle GAB$$?

Disclaimer: This was an olympiad problem. All credits to the one who originally made this problem.

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