In a satisfied, pleased, and peaceful manner; showing that you are happy with what you have.
From 'contented' (the adjective meaning satisfied) plus -ly (the adverbial suffix). 'Contented' comes from 'content' (to satisfy), ultimately from Latin contentus (contained, satisfied).
A cat purring by a window is 'contentedly' sitting there, and that visual perfectly captures the word—it's always used to describe people or animals who show peaceful, visible satisfaction.
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