"This/that angry" means "angry to this/that level" or "as angry as this/that", or when it's referring to the same person, "as angry as you are/were".
"So angry" can have the same meaning as "this/that angry" OR it can just mean "very angry":
Jane's car wasn't ready on time and she was so angry at the mechanics.
Here, she was very angry her car wasn't ready on time.
Jane's car wasn't ready on time and she was that angry at the mechanics.
This makes no sense because without something to compare it with, we don't know how angry she was.
Alice: "How angry was she?"
Bob: "Well, remember that time you forgot her passport? That angry."
Here it makes sense because "that angry" refers to a specific time.