Both "angry with" and "angry at" are found and used elsewhere. Many would say that "angry with" is the correct form and it came first in use, and that "at" came into use afterwards.
Some would also claim that "angry at" is because of the "mad at" a "cousin" expression.
Others would say that "at" is used when the focus is on the person not the situation then it´s "angry with", whereas when it´s directed to the situation itself then it would be "angry at".
The warriors in all of these fields have a point, it makes sense, but if you don´t know which is which you can use "angry at". Nobody is going to sue you for that.