On the anger scale, first comes annoyed, then vexed, then irate. When cartoon characters are irate, they're so mad that smoke comes out of their ears.
The first syllable of irate is ir for ire, related to the Greek word oistros which means "thing causing madness." An irate investor might sell all his or her stock in a company. Let's hope you thanked your aunt for the birthday check — otherwise you might get an irate phone call from her. When your mother is irate, you'd best get out of the way, and get busy cleaning your room.