The time by my watch is 10 minutes to 7, find the angle between the hour hand…

To find the angle between the hour hand and the minute hand at 10 minutes to 7 (which is 6:50), we can use the relative positions of the hands on the clock face.

Step-by-Step Analysis
Understand the Time: 10 minutes to 7 is 6:50.

Calculate the position of the minute hand:

The minute hand points at 10, which represents 50 minutes.

Since each minute mark is 6 degrees (360 degrees / 60 minutes), the minute hand is at 50 * 6 = 300 degrees from the 12 o'clock position.

Calculate the position of the hour hand:

The hour hand moves 30 degrees per hour (360 degrees / 12 hours) and 0.5 degrees per minute (30 degrees / 60 minutes).

At 6:50, the hour hand has moved past the 6 o'clock position.

Position = (6 hours * 30 degrees) + (50 minutes * 0.5 degrees) = 180 + 25 = 205 degrees from the 12 o'clock position.

Calculate the angle between them:

The difference = |300 degrees - 205 degrees| = 95 degrees.