vexed vs annoyed

vexed and annoyed both are adjectives.

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

As adjectives, vexed and annoyed are synonyms defined as:

vexed and annoyed: troubled persistently especially with petty annoyances

Other synonyms of vexed include harassed, harried, pestered.

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