What concept aids in finding the angle measure between the two hands of a clock reading 5:00 am?

To find the angle measure between the two hands of a clock at 5:00 am, knowing that each time increment on an analog clock measures 30 degrees is crucial.

At 5:00 am, the hour hand points directly at the 5 on the clock face. Since a full rotation of the clock represents 360 degrees and there are 12 hours on a clock, each hour represents 30 degrees (360 degrees divided by 12 hours). Therefore, to calculate the position of the hour hand, you simply multiply the hour (5) by 30 degrees:

5 hours × 30 degrees/hour = 150 degrees.

The minute hand at 5:00 am points at the 12, which is at 0 degrees. The angle between the hour hand at 150 degrees and the minute hand at 0 degrees is:

150 degrees - 0 degrees = 150 degrees.

This illustrates that knowing each hour increment is 30 degrees is essential for calculating the angles formed by the clock hands at any given time.