In a manner that shows strong disapproval or revulsion toward something.
From 'disgusted' (past participle of disgust, from Old French 'desgouster' meaning to turn away from in distaste) plus the adverbial suffix '-ly'. The prefix 'dis-' indicates reversal or negation, while 'gust' relates to taste.
The word 'disgust' literally means 'bad taste' in its original French form, so when you say something disgustedly, you're echoing a 700-year-old metaphor about how moral disapproval feels like a bad flavor in your mouth.
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