。
She seems to have taken offense at his words.
Literal
She [topic-は] his [genitive-の] words [at-に] mood [object-を] worsened [seems-ようだ].
気を悪くする ('take offense, get into a bad mood') is a set idiom — literally 'make one's mood bad,' using the Xを Yくする pattern with 気 ('mood, feeling, mind') as the X and 悪 ('bad') as the Y. The に on 言葉 marks the trigger of the offense. ~ようだ ('seems, appears') is the speaker's evidential conjecture based on observation — distinct from ~そうだ (appearance/hearsay), with subtle differences in evidential basis.