In an embarrassed manner; in a way that shows self-consciousness or shame.
From embarrassed (adjective) + '-ly' adverb suffix. The '-ly' suffix, from Old English, converts adjectives into adverbs describing the manner in which an action is performed.
The word 'embarrassedly' is somewhat rare because 'with embarrassment' often sounds more natural, but it's a grammatically perfect formation showing how the '-ly' suffix can attach to virtually any adjective in English.
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