Correct: Albert found himself very angry at Joanna.
Correct: Albert was very mad at Joanna.
Incorrect: Albert was mad with Joanna./ Albert found himself angry with Joanna.
That's a great example of how prepositions aren't always perfectly obvious and precise!
The example is complicated in the second instance (mad) because that word has two meanings: Angry and crazy.
Anyway, "angry at" is going to be very clear-- it means that Albert is angry/mad and that anger is aimed AT Joanna.
"Angry with" isn't so clear. (I grew up in the south, and I recognize that formation. Then again, we used to "brag on" our accomplishments, so "non-standard" was the common mode with prepositions.)
What will "angry with" mean to most people? "With" isn't aimed AT something. But it's about one noun "accompanying" another. "I am going to the store WITH John." So Albert being angry WITH Joanna could mean that they're both angry together (at someone else).
And "mad with" to me could mean "crazy about" (that is, in love with), so I'd probably avoid that altogether!
I figure it's usually best to go with the uncontestable option, the one no one will misinterpret.
What do you think? I'm looking for other examples of preposition situations where it just isn't incontrovertible which prep to use-- any examples?