"obliged to answer" is correct and usable in written English.
It is used to express an obligation to respond to something. For example, "She was obliged to answer the judge's questions."
"So Hamas feels obliged to answer back.
Instead, they are obliged to answer "on their honor".
That way, when visitors asked about the unseemly aberration, he would feel obliged to answer.
The prime minister is not obliged to answer, merely to say something.
When people ask me where I live, I feel obliged to answer: 'Elsewhere'.
One tactic that has become a favorite is submitting hundreds of written questions that the nominees are obliged to answer.
Courts are sometimes obliged to seek answers to questions about love that may well be unanswerable.
It is possible that this led the students to think that the question was not a binary choice and, as a result, they felt obliged to give answers that fell on a continuum.
This could act as a "fabrication check"—this concern becomes greater when informants are paid and may feel obliged to invent answers rather than to disappoint.
DEAR SIR, -- Your's of Aug. 3. came to hand yesterday; having had no moment to spare since, I am obliged to set down to answer it at a Committee table while the Committee is collecting.
