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No, lady gaga does not have an Adam's apple.
"...Adam's Apple-is a feature of the humanneck."
-Wikipedia
The Adam's apple got it's name in reference to the old Bible story of Adam of Eve. Adam's apple is a reference to the forbidden fruit Adam takes.
The thyroid cartilage.The thyroid cartilage forms the Adam's apple.
The correct terminology for the Adam's apple is the laryngeal prominence.