。
She was furious at his betrayal.
Literal
She [topic-は] his [genitive-の] betrayal [at-に] was-furious.
激怒する ('to be furious, fly into a rage') is one of the strongest anger verbs — 激 ('intense') + 怒 ('anger'). Reserved for very strong reactions; an everyday annoyance would call for 怒る instead. The に marks the cause of the rage. 裏切り is the noun form of 裏切る ('betray, double-cross'); literally 'cutting from the back/inside.'