Question 410535
each hour hand represents 1/12 of of a complete circle.


the number of degrees in a complete circle is 360 degrees.


each hour hand is therefore equal to 360 / 12 = 30


the 0 degree point is when the hour hand is on 12.


when the hour hand is on 1, the number of degrees from the 0 point is equal to 1 * 30 = 30.


when the hour hand is on 12, the number of degrees from the 0 point is equal to 12 I 30 = 360 degrees which is the same as 0 degrees because one complete revolution is equal to 360 degrees.


when the hour hand is on 5, the number of degrees from the 0 point is equal to 
5 * 30 = 150 degrees.


since there are 60 minutes between hours, when the time is 5:24, the hour hand is on 5 + 24/60.


24/60 is the same as .4


the hour hand is therefore on 5.4.


5.4 * 30 = 162 degrees.


now to the minute hand.


there are 12 * 5 minute marks on the clock.


that's a total of 60 minute marks.


each minute is therefore equal to 360/60 = 6 degrees.


when the little hand is on the 24 (4 minutes past the 4 o'clock mark), the number of degrees from the 0 point is equal to 24 * 6 = 144 degrees.


the angle between the little hand the the big hand is equal to 162 - 144 = 18 degrees.