An Olympiad Problem!

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 All credits to the one who originally made this problem.

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