In an angry, irritable, or bad-tempered manner; with annoyance or impatience.
From 'cross' (adjective, meaning bad-tempered, from Old Norse 'kross') + '-ly' (Old English suffix for adverbs). The adjective 'cross' originally meant ill-tempered by the 14th century.
The word 'cross' meaning angry probably comes from how people act when they're irritable—they seem to cut across others' moods sharply, like crossing lines in an angry way.
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