adverb
modifying a verb, adjective, or other adverb to describe how the action is performed
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The man was caught engaging in an adulterously relationship with his coworker.
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She was gossiping about her friend who was acting adulterously with someone else's spouse.
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I heard they were hooking up adulterously behind their partner's back.
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The company was accused of adulterously mixing their profits with illegal activities.