In a filthy, dirty, or morally corrupt manner; done in an unclean way.
From filthy (adjective, from Old English fylþ meaning dirt or impurity) + -ly (Old English -lice, meaning in the manner of). The -ly suffix transforms adjectives into adverbs showing how something is done.
Notice that when you add -ly to an adjective ending in -y (like filthy), you drop the y and add -ily—so filthy becomes filthily, not filthyly! These spelling rules developed over centuries to make words flow smoothly when spoken.
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