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

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).

Like any circle, a clock contains a total of . Because the clock face is divided into equal parts, we can find the number of degrees between each number by doing . At 5:00 the hour hand will be at 5 and the minute hand will be at 12. Using what we just figured out, we can see that there is an angle of between the two hands. We are looking for the larger angle, however, so we must now do .

You can think of a clock in two ways:

1. Out of 12 hours, or

2. In terms of a circle with

If you try to solve it in terms of #1:

Goal: Find the angle measurement between the hour and the minute hands. We only want to find the degrees between the hours of 9 and 12

So we are looking at 3 hours out of the 12 total hours on a clock.

As a fraction:

So that means that the clock hands are making an angle that is 1/4 of the clock (which is a circle). So knowing that a circle has in it,

1/4 of a circle is .

____________________________________________________________

2. If you think of the clock as a circle first you can determine the angle that the clock hands create very quickly.

Since there are in a circle, every hour that passes is a movement of . So knowing that, the clock will be moving 3 hours:

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, .

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

To solve this question recall that a clock is a cicle and a circle is comprised of 360 degress.

To find how many degrees lie between each of the twelve numbers on the clock, divide 360 by 12.

.

From here, we will multiply 30 degrees by 4 to find the degree angle of for the hands of the clock at 4:00.

Another approach is to simply divide 4 by 12 to determine what percentage of the circle the hands will cover, and then multiply that number by 360, which is the full degrees in a circle. Thus,

.

There are degrees in one complete revolution of a circle. There are minutes in one hour.

Create a fraction out of these two quantities to use later as a conversion rate:

Between the and there are minutes, so multiply this by the conversion rate to solve for the number of degrees: