What angle is formed by the hands of a clock at 920?

Answer 1

A clock dial divides the full 360-degree circle into 12 hours, so hours are 360/12 = 30 degrees apart. At 9:20 the minute hand points to "4." With the hour hand pointing to "9" the hands are separated by 5 hours (or 7 for the outside angle), which is 5*30 = 150 degrees.

The hour hand doesn't actually point to 9 at 9:20, however, having moved 20/60 minutes = 1/3 of an hour from 9 towards 10. If 1 hour is 30 degrees then 1/3 of an hour is 10 degrees. So the hands are 10 degrees farther apart, making the final answer 150 + 10 = 160 degrees.