The reflex angle between the hands of a clock at 10:25 is?

To find the reflex angle between the hands of a clock at 10:25, we need to determine the positions of the hour and minute hands.

1. The hour hand:

   • At 10:00, the hour hand points directly at the 10 on the clock.
   • Since 25 minutes have passed since 10:00, the hour hand would have moved a fraction of the way between the 10 and 11 on the clock.
   • To calculate this fraction, we divide the number of minutes passed (25) by the total number of minutes in an hour (60).
   • So, the hour hand would have moved (25/60) = 5/12 of the way between the 10 and 11.

2. The minute hand:

   • At 25 minutes past the hour, the minute hand points directly at the 5 on the clock.

3. Calculating the angle:

   • To find the reflex angle between the hour and minute hands, we need to calculate the difference between their positions.
   • Since the hour hand is between the 10 and 11, and the minute hand is at the 5, the difference is the angle between the 5 and the 11 on the clock.
   • The angle between each number on the clock is 30 degrees (360 degrees divided by 12).
   • So, the angle between the 5 and the 11 is (11 - 5) * 30 = 6 * 30 = 180 degrees.

4. Adjusting for the fraction of the hour hand:

   • Since the hour hand is not exactly at the 11, but 5/12 of the way between the 10 and 11, we need to adjust the angle.
   • The fraction of the hour hand's movement is (5/12) * 30 = 12.5 degrees.
   • Therefore, we subtract 12.5 degrees from the angle between the 5 and the 11.

5. Final calculation:

   • The reflex angle between the hands of the clock at 10:25 is 180 degrees - 12.5 degrees = 167.5 degrees.

So, the reflex angle between the hands of a clock at 10:25 is 167.5 degrees.