With “furious” or with “angry”, both prepositions sound correct! However, I would only say “mad at”, not “mad with”. (Unless you’re using “mad” in British English as a synonym for “crazy”—you could say “mad with envy”, for example)

Both "furious with" and "furious at" are commonly used expressions, and the choice between them depends on the context. Generally, they can be used interchangeably, but there might be subtle nuances in specific situations. "Furious with": This is often used when expressing anger or annoyance directed toward a person or entity. For example, "I am furious with my coworker for not completing the task." "Furious at": This is also used to express anger, but it can be directed toward a broader range of targets, including situations or events. For instance, "I am furious at the way the project was handled." In many cases, either preposition can be used without a significant change in meaning. It's more a matter of personal preference or the specific phrasing of the sentence.

I'm furious with you! correct I'm furious about that. correct I'm furious at you. incorrect

They are both fine. “At” is more directed, more confrontational.