She suddenly got angry.

Literal

She [topic-は] suddenly began-to-get-angry.

怒り出す is the inceptive compound 怒る + 出す, contrasting with the smoother 怒り始める. ~出す specifically marks abrupt or sudden onset, often involuntary — ideal here paired with 急に, doubling down on the suddenness. The English 'get angry' is event-focused, but Japanese 怒る often spans both 'become angry' (at an instant) and 'be angry' (the ongoing state, with ~ている). 怒り出す forces the inceptive reading: she went from calm to angry in a flash.