annoyed vs vexed

annoyed and vexed both are adjectives.

Word	Noun	Adjective	Verb	Adverb
annoyed	No	Yes	No	No
vexed	No	Yes	No	No

As adjectives, annoyed and vexed are synonyms defined as:

annoyed and vexed: troubled persistently especially with petty annoyances

Other synonyms of annoyed include harassed, harried, pestered.

annoyed (adjective)	vexed (adjective)
aroused to impatience or anger	causing difficulty in finding an answer or solution; much disputed
troubled persistently especially with petty annoyances	troubled persistently especially with petty annoyances