We generally aren't angry with concepts.
He was angry ____ how the government keeps raising taxes.
I'd use 'at' or 'about' here, not 'with'.
He was angry at the bad weather. - good
He was angry about the bad weather. - good
He was angry with the bad weather. - I'd avoid this. He's not actually angry with the weather itself, since the weather has no volition. He is simply angry because the weather is bad.
I think 'at' always works, whether you're angry with something or about something.