At 12:30, what is the degree measure of the smaller angle formed by the minute and hour hands of a circular 12-hour clock?

Answer 1

At 12:30, the hour hand should be half way between the 12 and the 1, right? If there are 12 spots on the clock, and it moved halfway through one of them, this means it has moved 1/24th of a rotation clockwise. I.e. 1/24th of 360°, which is 15°. The second hand will be pointing straight down at the 6, right? This is 180° away from the 12, but let us recall that the hour hand has moved 15° away from the 12 (towards the 6). So the smaller angle will be 180° - 15° = 165°. Yay math!