220 degrees
Which hand? The minute hand moves 360 degrees in 60 minutes which is 6 degrees per minute. So in 37 minutes it moves 37*6 = 222 degrees.
If we simply imagine the minute hand is on the 6, and the hour hand is on the two, there will be a total of 120 degrees between the minute and the hour hand, 1/3 of the clock is covered between the two hands. However, it is not that simple. Because 30 minutes has travelled, the hour hand will be half way between the 2 and the 3. We know that every hour, the hour hand moves 30 degrees (360 / 12 hours = 30). Therefore, in 30 minutes, it will have travelled 15 degrees. Which means the hour hand is 15 degrees closer to the minute hand. Therefore, the actual angle between the minute and hour hand is actually 105 degrees.
This problem can be solved as follows: The angle Ah of the hour hand of a clock, measured from the position at noon or midnight when the hour and minute hands exactly coincide, is Ah = (360 degrees/12 hours)th, where th is the time in hours, including fractions of hours, because the hour hand moves the entire 360 degrees around the clock in 12 hours. Similarly, the angle Am of the minute hand = (360 degrees/60 minutes)tm, where tm is the time in minutes only, including fractions of minutes. The stated time is 3 + 40/60 + 20/3600 hours = 3.672222... hours and the angle is therefore about 110. 11666666... degrees, using the formula above. The time in minutes only is 40 + 20/60 = 40.33333...., so that the angle of the minute hand is 242 degrees. The difference between them is therefore about 131.833..... degrees, or in fraction form 131 and 5/6.
I have worked out that of course a full rotation is 360° and due to there being 12 hours on a clock this relates to 360/12 = 30°. So each hour represents 30°. The minute hand moves 60s per minute and a full rotation is 360° so: 360/60 + 6° per minute. So in 20 minutes the minute hand will be 6 * 20 + 120° and the hour hand will be 120/12 = 10°. Just checking if my math is correct. If it is incorrect please could you elbarote on this puzzle. Thanks
Oh, dude, you're hitting me with the clock riddles now? Alright, let's see... The hour hand moves 30 degrees every hour, so it'll be at 90 degrees four times between 9am and 3pm. The minute hand will be at 90 degrees once every hour, so that's five times total. So, like, five times in total, I guess.
6 degrees.
It moves through 360 degrees
Assuming the hour hand moves steadily for the entirety of the hour, the angle formed by the hour and minute hand would be 55 degrees.
The minute hand in a clock in most cases sweeps 360 degrees every hour. So in one minute the angle swept is 360/60 = 36/6 = 6 degrees
On a normal 12-hour clock, the minute hand moves thru 360° in 1 hour, 360° in 60 minutes, or 6° every minute. In ten seconds, the minute hand moves 1°.
60 degree angle at 4:12 At 4.00 the angle is 120 degrees. In 12 minutes the minute hand moves 72 degrees while the hour hand moves 6 degrees. So that 120 degree angle reduces by 66 degrees in 12 minutes, and the answer is 54 degrees.
The hour hand moves 360/12=30 degrees every hour (so in 12 hours it moves 360 degrees -- back to where it started). One minute is 1/60 of an hour, so in 1 minute the hour hand moves 30/60=1/2 degree. In the meantime the minute hand has moved 1/60th of the distance around the clock, or 1/60 x 360 = 6 degrees. So at 12:01 the angle between the hands is 6 - 1/2 = 5 1/2 degrees
it moves at one click every 60 seconds
180 degree angle
Every minute on a clock is 6 degrees, making every five minutes where the numbers are 30 degrees. In theory, hands on the 1 and 6 would would show an angle of 150 degrees. In actuality, the hour hand moves halfway between the 1 and 2 by 1:30 making the angle 135 degrees.
Hour hand moves 30 degrees, minute hand moves 360 degrees.
At 6:00, the hands are 180° apart. In the thirty minutes it takes the minute hand to reach the six, the hour hand will have advanced 15° from the six because it moves at a rate of ½° each minute.