As a general rule, I’d say there is no reason to think that an idiomatic phrase like “The sky is angry” in English would directly/literally translate into an unrelated language like Japanese. I’ll leave it to someone else to come up with the Japanese equivalent and maybe prove me wrong in this case.
Now:
You can’t use 怒った and です together. Your conjugation requires 怒った or 怒りました or 怒っていた or 怒っていました.
“She seems angry.” - 彼女が怒っているように見えます is a formal possibility. 彼女が怒っているっぽい is a real informal option.
I don’t know what it’s supposed to be, but the wisdom dictionary actually has an entry for “an angry sky” (!?):
険悪な空模様
Explanation:
2(文)[通例名の前で]荒れ模様の, 荒れ狂った<空・海>