One past-tense conjugation only, please. :) "Did he use to be jealous of you?" This is how you put "used to be" in a question - note the past tense is indicated with "did", so "use" stays in a base form.

Did he use to be jealous of you?

Yes, it is. BTW, every sentence you read in that book of yours is grammatically correct. Don't you trust the writer?