Ask yourself the question. I think someone gets annoyed by something when they get too much of it or if it's something they don't like.
to be annoyed with someone or something
Maybe he was stressed out about something else?
That depends on whether he is rightfully annoyed or not. You don't say how his annoyance arose. If you have something to apologise for, and you are sorry for it, then apologise. If his annoyance is unjustified, let him stew. Do not apologise for something you did not do, or to which he is misreacting.
To be vexed would be to be confronted with a problem that was difficult to deal with, causing disagreement and some argument. You would be irritated and annoyed
You're being annoyed/bothered by something/someone.
To get 'worked up about' something is to get upset, excited, irritated, annoyed.
It is the point where a person notices something and becomes annoyed.
Yes, "cross" can also mean annoyed or angry, especially in British English. It is used to describe someone who is irritated or upset about something.
It means she believes you did something stupid that annoyed her.
simply do something because people find it hard haha I hope i annoyed you.
Indignation
In human relations, irritation threshold is the point at which someone notices something and gets annoyed.