こたえる is always preceded by a に。In the Japanese language, the act of answering is thought of as "answering to" something instead of just "answering something," which might explain why "に" is used instead of "を"
I think an example that might make the particles clear might be something like 「私は第三の質問に月曜日をかえりました。」
I answered "Monday" to question number 3.
I might be wrong, so if anyone more experiencedwith Japanese wants to come in, it would be appreciated.
質問に三つ would be the alternative ordering, not は, but it changes the meaning slightly - this would be "please answer three questions", possibly implying out of more than three, versus the duo sentence "please answer the three questions".