In the diagram $\overleftrightarrow{\mathit{\text{AB}}}$bisects $\angle DHF$, $\overleftrightarrow{\mathit{\text{AB}}}\mathit{\perp }\overline{\mathit{\text{GH}}}$, $\overleftrightarrow{\mathit{\text{AB}}}\mathit{\parallel }\overleftrightarrow{\mathit{\text{CD}}}$, and $m\angle AHD=60°$. Find the measure of each angle.

$‎\angle AHG$.

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