That made me really angry.

that Determiner

— Used to show which thing we are talking about; used with things that are not close to the speaker. Give me that book, not this one. Give me that, not this. That dog is hungry.

that Subordinator

— used to link a subordinate clause to a main one You said that you liked me. Give me the book that I dropped.

made

— adjective produced by a manufacturing process bought some made goods at the local store; rope and nails — adjective (of a bed) having the sheets and blankets set in order a neatly made bed — adjective successful or assured of success now I am a made man forever — Christopher Marlowe

me Pronoun

— You use me instead of your name, to refer to yourself. This is my book. It belongs to me.

really Adverb

— When something is really a certain way, its very or very much that way. I really want to see a film. I'm really hungry now. You did a really good job on that. Thank you for coming and helping me this morning. I really appreciate it. I don't really like Japanese food. — If something really exists or really happens, it does exist or happen. Are you really going to the show? Yes, I really will be there.

really Interjection

— You can say "really?" when you are surprised. "He won yesterday." "Really?" — You can say "really" when you agree with something. "That girl talks about herself way too much." "Really. She's a nightmare."

angry Adjective

— red, and infected. He had an angry wound.