Hypophora: Figure of reasoning in which one or more questions is/are asked and then answered, often at length, by one and the same speaker; raising and responding to one's own question(s).

Examples

"When the enemy struck on that June day of 1950, what did America do? It did what it always has done in all its times of peril. It appealed to the heroism of its youth."

 -- Dwight D. Eisenhower, I Shall Go to Korea Address

"How many men ever went to a barbecue and would let one man take off the table what they intended for 9/10 of the people to eat? The only way you'll ever be able to feed the balance of the people is to make that man come back and bring back some of that grub he ain't got no business with."

-- Huey P. Long, Address to Senate Staffers

"It is almost preposterous on my part to advocate your loyalty to Franklin D. Roosevelt. And why, may I ask you? Simply because the money-changers are being driven from the temple. Simply because the outworn gold standard which held you and myself in bondage for generations has evaporated into the mists of the past."

-- Father Charles Coughlin, Roosevelt or Ruin

"Our people have had more happiness and prosperity over a wider area for a longer time than men have ever had since they began to live in ordered societies 4000 years ago. Since we have come so far, who shall be rash enough to set limits on our future progress? Who shall say that since we have gone so far, we can go no farther? Who shall say that the American dream is ended? For myself, I believe that all we have done upon this continent is but a prelude to a future in which we shall become not only a bigger people but also a wiser people, a better people, an even greater people."

-- Adlai Stevenson, 1952 Campaign Speech

Note: Can you spot the epistrophe? 

"What is George Bush doing about our economic problems? Now, four years ago he promised 15 million new jobs by this time -- and he’s over 14 million short. Al Gore and I can do better. He has raised taxes on the people driving pickup trucks and lowered taxes on the people riding in limousines. We can do better."

 -- William Jefferson Clinton, 1992 DNC Acceptance Address

Note: Can you spot the antithesis? 

"In 1982, corporate growers gave [George] Deukmejian one million dollars to run for governor of California. Since he took office, Deukmejian has paid back his debt to the growers with the blood and sweat of California farm workers. Instead of enforcing the law as it was written against those who break it, Deukmejian invites growers who break the law to seek relief from governor's appointees. What does all this mean for farm workers? It means that the right to vote in free elections is a sham. It means the right to talk freely about the union among your fellow workers on the job is a cruel hoax. It means that the right to be free from threats and intimidation by growers is an empty promise. It means that the right to sit down and negotiate with your employer as equals across the bargaining table and not as peons in the fields is a fraud. It means that thousands of farm workers, who are owed millions of dollars in back pay because their employers broke the law, are still waiting for their checks. It means that 36,000 farm workers, who voted to be represented by the United Farm Workers in free elections, are still waiting for contracts from growers who refuse to bargain in good faith. It means that for farm workers child labor will continue. It means that infant mortality will continue. It means that -- It means that malnutrition among children will continue. It means the short life expectancy and the inhuman living and working conditions will continue."

-- Cesar Chavez, Commonwealth Club Address

Note: Also anaphora ("It means that....") and antithesis ("...as equals across the bargaining table and not as peons in the fields.")