Question 603010
Determine the smaller angle between the hands of a clock at 12:20. Show or explain how you got your answer.
<pre>
Here's another approach which amounts to the same thing as the other
tutor's explanation, but may be easier for some people to inderstand:

The hour hand makes 360° in 12 hours, so
the angle speed of the hour hand is 360/12 or 30 degrees/hour.

The minute hand makes 360° in 1 hour, so
the angle speed of the minute hand is 360 degrees/hour. 

The hands were together at 12:00.  12:20 is 20 min. or 1/3 hr.
later.  So in that 20 minutes or 1/3 hr., 

the hour hand has swept through (1/3 hr)×(30degrees/hr) or 10 degrees,

and

the minute hand has swept through (1/3 hr)×(360degrees/hr) or 120 degrees.

Therefore the angle between them at 12:20 is 120°-10° or 110°
 
Edwin</pre>