Final answer:
The times when the hour hand and minute hand form a 0° angle on a clock, signifying they overlap, only occur once between each hour segment. While 12:00 is one of these times, the next actual occurrences are a little past 1:05 and 7:05, which would round to approximately 1:30 and 7:30, making option D the best choice among the given options, even though it's not the precise answer.
Step-by-step explanation:
The question asks about the times when the hour hand and minute hand form a 0° angle on a clock face, which means they are perfectly overlapped. At 12:00, this is undoubtedly the case, as both hands are at the 12. However, contrary to some initial assumptions, 6:00 does not feature an alignment of the hands, because at 6:00, the hour hand is precisely on 6 while the minute hand is on 12. Similarly, at both 3:00 and 9:00, the hour hand and the minute hand are 90° apart, not overlapped.
Let's consider option C: At 2:00, the hour hand is not perfectly on the 2, but slightly past it, because it moves as the minutes pass. It would be similar for 8:00. But the truth is, the only other time the hands overlap exactly (forming a 0° angle) after 12:00 is a little past 1:05 and again a little past 7:05, because the minute hand moves 12 times faster than the hour hand.
Hence, the correct answer is not listed explicitly among the provided choices. However, if we consider the mechanism of the clock's motion and round to the nearest half hour, the closest approximations to when the hands overlap again would be 1:30 and 7:30. Therefore, option D is the most accurate of the given choices.