。
She got irritated at being asked such a silly question.
Literal
She [topic-は] [silly-馬鹿らしい] question [object-を] was-asked-and got-irritated.
A passive-of-suffering: 質問をされて — 'had a question asked of her' — emphasizes she was on the receiving end of an unwanted action. Japanese passives often carry this 迷惑の受身 (adversative) flavor where the subject is negatively affected. 馬鹿らしい uses the suffix ~らしい to derive an adjective from 馬鹿: 'foolish, ridiculous' (something resembling 馬鹿's quality). いらいらする is a productive mimetic + する verb for getting irritated.