At 11:00 a.m. how many degrees are in the smaller angle formed by the minute hand and the hour hand of the clock?
To solve this problem, I need to figure out how many degrees each hand moves in one hour and then how many degrees they have moved by 11:00 a.m. I know that the minute hand moves 360 degrees in one hour, so it moves 6 degrees in one minute. The hour hand moves 360 degrees in 12 hours, so it moves 30 degrees in one hour. At 11:00 a.m., the minute hand is at the 12 o'clock position, which I can call 0 degrees, and the hour hand is at the 11 o'clock position, which is 330 degrees. The difference between 0 and 330 degrees is 330 degrees, but that's not the smaller angle I'm looking for. The smaller angle is the complement of that, which is 360 - 330 = 30 degrees. So the answer is 30 degrees. 