Voting to close and answering is indeed inconsistent, since the reason we close questions is that we assert that they cannot be answered (or at least that they cannot be answered well).
Closed questions are noise, and meant to be deleted (after giving time for the closure to be contested). Writing an answer when you know that it is satisfactory wastes not only your time, but the time that readers will spend on it. Furthermore, it gives the unwelcome signal that it's ok to ask these questions, since somebody answered — which might carry weight on a forum, but doesn't on a site geared towards content with lasting value, yet this is used as an argument to whine about closure. The only reason I can think of to answer and close is to farm reputation for the answer, which is anti-social behavior in itself. Don't do it.
The one exception is voting to close as off-topic when you expect the question to be migrated to another site. Then it's ok to answer as you would if the question had been posted on the other site.
It's ok if you change your mind, of course. It's can also happen that the question was edited in the meantime, in a way that changes your judgement about its answerability.