Clock Math - PSAT Math
Card 1 of 42
If it is 2:00 PM, what is the measure of the angle between the minute and hour hands of the clock?
If it is 2:00 PM, what is the measure of the angle between the minute and hour hands of the clock?
Tap to reveal answer
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.
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.
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What is the measure, in degrees, of the acute angle formed by the hands of a 12-hour clock that reads exactly 3:10?
What is the measure, in degrees, of the acute angle formed by the hands of a 12-hour clock that reads exactly 3:10?
Tap to reveal answer
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°.
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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?
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?
Tap to reveal answer
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).
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).
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It is 4 o’clock. What is the measure of the angle formed between the hour hand and the minute hand?
It is 4 o’clock. What is the measure of the angle formed between the hour hand and the minute hand?
Tap to reveal 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
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
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If a clock reads 8:15 PM, what angle do the hands make?
If a clock reads 8:15 PM, what angle do the hands make?
Tap to reveal answer
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.
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.
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What is the measure of the smaller angle between the hands of a clock if the time reads 
?
What is the measure of the smaller angle between the hands of a clock if the time reads
Tap to reveal answer
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
.
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
The angle between the
Finally, we must figure out exactly how far past the
Therefore, our hour hand has moved an extra
Our angle is equal to
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What is the measure, in degrees, of the acute angle formed by the hands of a 12-hour clock that reads exactly 3:10?
What is the measure, in degrees, of the acute angle formed by the hands of a 12-hour clock that reads exactly 3:10?
Tap to reveal answer
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°.
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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?
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?
Tap to reveal answer
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).
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).
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If it is 2:00 PM, what is the measure of the angle between the minute and hour hands of the clock?
If it is 2:00 PM, what is the measure of the angle between the minute and hour hands of the clock?
Tap to reveal answer
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.
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.
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It is 4 o’clock. What is the measure of the angle formed between the hour hand and the minute hand?
It is 4 o’clock. What is the measure of the angle formed between the hour hand and the minute hand?
Tap to reveal 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
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
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If a clock reads 8:15 PM, what angle do the hands make?
If a clock reads 8:15 PM, what angle do the hands make?
Tap to reveal answer
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.
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.
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What is the measure of the smaller angle between the hands of a clock if the time reads ?
What is the measure of the smaller angle between the hands of a clock if the time reads
Tap to reveal answer
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
.
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
The angle between the
Finally, we must figure out exactly how far past the
Therefore, our hour hand has moved an extra
Our angle is equal to
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If it is 2:00 PM, what is the measure of the angle between the minute and hour hands of the clock?
If it is 2:00 PM, what is the measure of the angle between the minute and hour hands of the clock?
Tap to reveal answer
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.
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.
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What is the measure, in degrees, of the acute angle formed by the hands of a 12-hour clock that reads exactly 3:10?
What is the measure, in degrees, of the acute angle formed by the hands of a 12-hour clock that reads exactly 3:10?
Tap to reveal answer
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°.
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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?
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?
Tap to reveal answer
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).
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).
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It is 4 o’clock. What is the measure of the angle formed between the hour hand and the minute hand?
It is 4 o’clock. What is the measure of the angle formed between the hour hand and the minute hand?
Tap to reveal 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
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
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If a clock reads 8:15 PM, what angle do the hands make?
If a clock reads 8:15 PM, what angle do the hands make?
Tap to reveal answer
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.
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.
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What is the measure of the smaller angle between the hands of a clock if the time reads ?
What is the measure of the smaller angle between the hands of a clock if the time reads
Tap to reveal answer
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
.
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
The angle between the
Finally, we must figure out exactly how far past the
Therefore, our hour hand has moved an extra
Our angle is equal to
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What is the measure, in degrees, of the acute angle formed by the hands of a 12-hour clock that reads exactly 3:10?
What is the measure, in degrees, of the acute angle formed by the hands of a 12-hour clock that reads exactly 3:10?
Tap to reveal answer
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°.
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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?
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?
Tap to reveal answer
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).
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).
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