Student or Learner
Is this correct..?
You are angry with a person and angry at a thing.
He was angry at his own inability to express his feelings.
Here his 'inability' is rather the cause of his anger than its 'object' in the normal sense, so that 'angry about' could also be used here with no appreciable difference in meaning.
Informally, also, 'angry at' is sometimes used with people, whereas 'angry with' is the more standard expression.
Occasionally, however, one may even be angry with something, if that thing is a physical object towards which anger is directed exactly as if towards a person, e.g.
There's no point getting angry with your car and shouting at it just because it won't start the first time!