。
She's very angry with him.
Literal
She [topic-は] him [object-を] very is-being-angry.
怒る has two case patterns: ~に怒る ('be angry at') and ~を怒る ('scold someone, be angry at someone'). The を pattern here, combined with のこと ('the matter of him'), reads as 'be very angry about him.' The ~ている marks the ongoing emotional state. Without のこと, just 彼を怒っている could lean closer to 'is scolding him.'