Wiktionary
n. (context rhetoric English) A device in which the author poses a question which is in turn answered.
Wikipedia
Hypophora, also referred to as anthypophora or antipophora, is a figure of speech in which the speaker poses a question and then answers the question. Hypophora can consist of a single question answered in a single sentence, a single question answered in a paragraph or even a section, or a series of questions, each answered in subsequent paragraphs. Hypophora is used (1) as a transitional device, to take the discussion in a new direction, (2) a device to stimulate interest, since a reader's curiosity is stimulated by hearing a question, and (3) to suggest and answer questions the reader might not have thought of.