# PSAT Math : How to find the angle of clock hands

## Example Questions

### Example Question #1 : How To Find The Angle Of Clock Hands

If is 2:00 PM, what is the measure of the angle between the minute and hour hands of the clock?

120 degrees

90 degrees

60 degrees

45 degrees

30 degrees

60 degrees

Explanation:

First note that a clock is a circle made of 360 degrees, and that each number represents an angle and the separation between them is 360/12 = 30. And at 2:00, the minute hand is on the 12 and the hour hand is on the 2.  The correct answer is 2 * 30 = 60 degrees.

### Example Question #2 : How To Find The Angle Of Clock Hands

It is 4 o’clock.  What is the measure of the angle formed between the hour hand and the minute hand?

Explanation:

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

### Example Question #1 : How To Find The Angle Of Clock Hands

If a clock reads 8:15 PM, what angle do the hands make?

Explanation:

A clock is a circle, and a circle always contains 360 degrees. Since there are 60 minutes on a clock, each minute mark is 6 degrees.

The minute hand on the clock will point at 15 minutes, allowing us to calculate it's position on the circle.

Since there are 12 hours on the clock, each hour mark is 30 degrees.

We can calculate where the hour hand will be at 8:00.

However, the hour hand will actually be between the 8 and the 9, since we are looking at 8:15 rather than an absolute hour mark. 15 minutes is equal to one-fourth of an hour. Use the same equation to find the additional position of the hour hand.

We are looking for the angle between the two hands of the clock. The will be equal to the difference between the two angle measures.

### Example Question #1 : How To Find The Angle Of Clock Hands

What is the measure of the smaller angle formed by the hands of an analog watch if the hour hand is on the 10 and the minute hand is on the 2?

56°

90°

45°

30°

120°

120°

Explanation:

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).

### Example Question #21 : Circles

What is the measure of the smaller angle between the hands of a clock if the time reads ?

Explanation:

First, we must determine where the hands are located at this time. The minute hand will be exactly on the three. The hour hand will be a little bit (15 mins) passed the seven. A circle has  in it, so because there are  numbers on a clock's face, each number is separated by

The angle between the  and the  is equal to

Finally, we must figure out exactly how far past the  our hour hand is. If the hour hand moves  in , that means that it must move a half of a degree every minute. If we are  past , we can do

Therefore, our hour hand has moved an extra  due to the  that have elapsed.

Our angle is equal to

.

### Example Question #1 : How To Find The Angle Of Clock Hands

What is the measure, in degrees, of the acute angle formed by the hands of a 12-hour clock that reads exactly 3:10?

60°

35°

65°

55°

72°