Asking oneself a question and answering it oneself; thinking something through internally or soliloquizing.
将来について自問自答した結果、大学院に進むことに決めた。
After asking and answering himself about his future, he decided to go on to graduate school.
会議中、彼は小声で自問自答しているようだった。
During the meeting he seemed to be asking and answering himself under his breath.
重要な決断の前にはしばらく自問自答する時間を持つといい。
Before an important decision, it's good to take some time to ask and answer yourself.