Within the trapezoid ABCD, where AB=BC=CD, select points E and F along the base AD such that AE=EF=FD. The extensions of segments BE and CF intersect at point G, and the extensions of segments AB and
DC intersect at point H. With the angle AGD measuring 50 degrees, determine the measure of angle AHD.

Trapezoid's embrace holds

Equal lengths, points aligned true

G and H converge,

Angles weave a geometric tale,

AHD's secret, AGD's clue.

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