In a manner that causes embarrassment or shame; so as to be embarrassing.
From embarrassing (present participle/adjective) + '-ly' adverb suffix. This creates an adverb from the '-ing' form of the verb, which is a productive pattern in English (confusingly, amusingly, etc.).
We often say 'embarrassingly bad' or 'embarrassingly obvious,' using this adverb to modify adjectives rather than verbs—this flexibility shows how English adverbs have evolved to function in multiple grammatical positions beyond the traditional 'verb modifiers.'
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