In a pleasant, acceptable, or mutually satisfying way; with willingness and good nature.
From agreeable + -ly (adverbial suffix). Agreeable itself comes from agree via the -able suffix, meaning 'capable of agreeing' or 'pleasing.'
You'll see 'agreeably' constantly in 19th-century literature—Jane Austen and her contemporaries loved this word. It conveyed not just politeness but a social satisfaction: 'We passed the evening agreeably' means it was harmonious, pleasant, and socially correct.
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