。
She looked at my face as if she were angry.
Literal
She [topic-は] got-angry [as if-ように] my face [object-を] looked-at.
おこったように uses ~ように to mark manner — 'as if angry.' The sentence is written entirely in hiragana for おこった (怒った) and みた (見た), which is common in casual writing or when the kanji isn't needed for disambiguation. The key point is that she's not confirmed angry — ~ように only says it looked that way, leaving room for the possibility that her expression was misread.