Here are some adjectives that we use that mean angry. They are show strong anger. They can be used in any situation - none of them are slang.
Here are some idioms that can be used in angry situations
To look angry / to have an angry appearance:
"Stay away from Mr.Thomas, he's got a face like thunder. I don't know what happened to make him so angry."
To get very angry and fly into a rage:
"He hit the roof when I told him that someone had scratched his car."
Something that makes you angry drives you crazy:
"It drives me crazy when people talk loudly in the cinema."
Here are some commonly used slang expressions that show someone is angry. These are casual expressions and should not be used in formal situations. They all mean the same thing: "She became angry."
Link: How to let people know you find something annoying