### All ACT Math Resources

## Example Questions

### Example Question #1 : Clock Math

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

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

30°

45°

56°

90°

120°

**Correct answer:**

120°

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.)

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

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)

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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)

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

35°

60°

72°

65°

55°

**Correct answer:**

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°.

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