The entire clock measures 360°. As the clock is divided into 12 sections, the distance between each number is equivalent to 30° (360/12). The distance between the 2 and the 3 on the clock is 30°. One has to account, however, for the 10 minutes that have passed. 10 minutes is 1/6 of an hour so the hour hand has also moved 1/6 of the distance between the 3 and the 4, which adds 5° (1/6 of 30°). The total measure of the angle, therefore, is 35°.

The entire clock measures 360°. As the clock is divided into 12 sections, the distance between each number is equivalent to 30° (360/12). The distance between the 2 and the 3 on the clock is 30°. One has to account, however, for the 10 minutes that have passed. 10 minutes is 1/6 of an hour so the hour hand has also moved 1/6 of the distance between the 3 and the 4, which adds 5° (1/6 of 30°). The total measure of the angle, therefore, is 35°.

At four o’clock the minute hand is on the 12 and the hour hand is on the 4. The angle formed is 4/12 of the total number of degrees in a circle, 360.

4/12 * 360 = 120 degrees

At four o’clock the minute hand is on the 12 and the hour hand is on the 4. The angle formed is 4/12 of the total number of degrees in a circle, 360.

4/12 * 360 = 120 degrees

The path traveled by the tip of the minute hand over the course of one hour is a circle of radius . The circumference of that circle is

.

The tip has traveled 10 inches since noon, so the fraction of the circle traveled is ,

and the number of minutes that have expired since noon is .

Therefore, to the nearest minute, the time is 12:16.

The path traveled by the tip of the minute hand over the course of one hour is a circle of radius . The circumference of that circle is

.

The tip has traveled 10 inches since noon, so the fraction of the circle traveled is ,

and the number of minutes that have expired since noon is .

Therefore, to the nearest minute, the time is 12:16.

There are 360 degrees in a circle. If you divide that by four then you get 90 degrees and if you divide 60 minutes by 4 you get 15 minutes. Therefore every 15 minutes on a clock represents 90 degrees. If I go clockwise from 12 there are 45 minutes or three lots of 15 minutes. If 1 lot of 15 minutes equals 90 degrees then,

The minute hand will be on the number 9, which would form a 90-degree angle with an hour hand pointing right at 12.

The hour hand has moved three-quarters, or 75% of the way from 12 to 1. Since the full 360 degrees of the circle represents 12 hours, the segment representing the hour between 12 and 1 is

.

75% of that is

.

The total angle is the 90 degrees between 9 and 12, and the additional 22.5 degrees, or

It is important to recall that a clock is a circle and a circle is comprised of 360 degrees. Therefore, to calculate how many degrees are between the 12 and the 3 we need to set up a ratio.

The degree measure between each number is,

.

Therefore, to find the degree measure for three numbers would be,

.

If the hour hand is on the 12 and the minute hand is on the 3 it would create a right angle which is, .

A analog clock is divided up into 12 sectors, based on the numbers 1–12. One sector represents 30 degrees (360/12 = 30). If the hour hand is directly on the 10, and the minute hand is on the 2, that means there are 4 sectors of 30 degrees between then, thus they are 120 degrees apart (30 * 4 = 120).