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

## Example Questions

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### Example Question #1 : 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

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?

30°

90°

45°

56°

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 #1 : How To Find The Angle Of Clock Hands

Using the 8 hour analog clock from question 1 (an analog clock with 8 evenly spaced numbers on its face, with 8 where 12 normally is), what is the angle between the hands at 1:30? (Note: calculate the smaller angle, the one going between the hour and minute hand in a clockwise direction.)

Explanation:

Because it's an 8 hour clock, each section of the clock has an angle of 45 degrees due to the fact that .

When the clock reads 1:30 the hour hand is halfway in between the 1 and the 2, and the minute hand is on the 4 (at the bottom of the clock). Therefore, between the hour hand and the "2" on the clock there are  degrees and between the 2 and the 4 there are  degrees. Finally,

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

How many degrees are in each hour-long section of an analog clock with 8 equally spaced numbers on the face?

Explanation:

If creating a picture helps, draw a circle and place 8 at the top where 12 normally is. Then put 2, 4, and 6 at the positions of 3, 6, and 9 on a normal 12-hour analog clock. 1, 3, 5, and 7 go halfway in between each even number.

Now, because each section is equally spaced, and because there are 8 sections we simply divide the total number of degrees in a circle () by the number of sections (8). Thus:

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

What is the angle between the hands of a standard 12-hour digital clock when it is 8:15? (note, give the smaller of the two angles, the one between the hands going clockwise

Explanation:

When the clock reads 8:15 the minute hand is on the 3 and the hour hand is just past the 8.

Each section of the clock is

degrees.

From 3 to 8 then there are 150 degrees. However, the hour hand has moved a quarter of the way between the 8 and the 9, or a quarter of 30 degrees.  and so

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

What is the measure of the angle between the hands of a clock at ? (compute the angle going clockwise from the hour hand to the minute hand)

Explanation:

Each section of the clock is , and by  the hour hand has gone three quarters of the way between the  and the . Thus there are  between the hour hand and the  numeral. The minute hand is on the , and there are  between the  and the . So in total there are  between the hands

### Example Question #5 : How To Find The Angle Of Clock Hands

On a  analog clock (there is a  where the  normally is, a  in the normal position of the , with  where the  is on a standard  analog, the  where the  is on a standard analog, and  and  are at the spots normally occupied by  and  respectively), what is the angle between the hands when the clock reads

Explanation:

The number of degrees between each numeral on the clock face is equal to the number of degrees in a circle divided by the number of sections:

At  the  hand has gone  way through the  between the and the . Thus there are only  left between it and the 3. There are 120 degrees between the 3 and the 5, where the minute hand is, so the total amount of degrees between the hands is:

### Example Question #6 : How To Find The Angle Of Clock Hands

What is the angle between the clock hands when the clock reads 6:30?

Explanation:

Remember there are  in each hour long section of the clockface

.

When the clock reads 6:30 the minute hand is on the 6, and the hour hand is halfway between the 6 and 7.

Thus the number of degrees between the hands is

### Example Question #7 : How To Find The Angle Of Clock Hands

On a  analog clock (with a  where the  normally is and a  where the  normally is) what is the angle between the hands when the clock reads ? (Give the smaller of the two angles)

Explanation:

When the clock reads  on this clock, the hour hand will be  of the way between the  and the . Since there are , evenly sized, sections of this clock each section has:

. And . At  the minute hand will be one-quarter of the way around the entire dial.
Thus the hands are  from each other

### 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?

65°

72°

35°

60°

55°