What should I do when my girlfriend hangs up on me out of anger?

I would just call her back and say "Hey, I'm sorry I upset you, I need to blow off some steam can I call you tomorrow?" Just try to say it in the best way possible to show her that you aren't mad at her. If that doesn't work: you are stuck talking everything out right there and then.

Call her back and apologize for whatever you said was wrong.. And if she doesn't answer your phone calls, leave her a message saying your sorry.. And when us girls hang up because we are mad at the guy, we really want to see if you would chase after us or not.. Cause some girls like to test guys and see if they really care for them or not.. And if you don't call back, then that's how we know you really don't care.. But just call her and if she doesn't answer, leave her a message apologizing, and tell her, you'll let her cool off, and that maybe you two can work everything out tomorrow.. : )

Call her back,
I love it when I'm mad then they call me back.
but that's just me.

blow her phone up till she picks up.. and tell not to be rude.. =]