How to find the angle of clock hands - ISEE Upper Level Quantitative Reasoning
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The clock in the classroom reads 5:00pm. What is the angle that the hands are forming?
The clock in the classroom reads 5:00pm. What is the angle that the hands are forming?
Since the clock is a circle, you can determine that the total number of degrees inside the circle is 360. Since a clock has 12 numbers, we can divide 360 by 12 to see what the angle is between two numbers that are right next to each other. Thus, we can see that the angle between two numbers right next to each other is 
. However, the clock is reading 5:00, so there are five numbers we have to take in to account. Therefore, we multiply 30 by 5, which gives us 
as our answer.
Since the clock is a circle, you can determine that the total number of degrees inside the circle is 360. Since a clock has 12 numbers, we can divide 360 by 12 to see what the angle is between two numbers that are right next to each other. Thus, we can see that the angle between two numbers right next to each other is
Compare your answer with the correct one above
The time on a clock reads 5:00. What is the measure of the central angle formed by the hands of the clock?
The time on a clock reads 5:00. What is the measure of the central angle formed by the hands of the clock?
First, remember that the number of degrees in a circle is 360. Then, figure out how many degrees are in between each number on the face of the clock. Since there are 12 numbers, there are 
between each number. Since the time reads 5:00, multiply 
, which yields 
.
First, remember that the number of degrees in a circle is 360. Then, figure out how many degrees are in between each number on the face of the clock. Since there are 12 numbers, there are
Compare your answer with the correct one above
At which of the following times on a clock is the smaller angle created by the minute hand and hour hand NOT less than 
?
At which of the following times on a clock is the smaller angle created by the minute hand and hour hand NOT less than
In this problem, you are working with the shape of a clock. A clock is in the shape of a circle, which has 
total. You are looking for the time for which the smaller angle created by the minute and hour hands is NOT less than 
- in other words, the time must create an angle greater than 
.
First, it's helpful to recognize at what times a right angle (
) exists. This would be 3:00 and 9:00. It's also useful to recognize that times such as 3:30 and 9:30 will be slightly under 
- the hour hand moves just past the 3 and 9 on a clock at these times to create this effect. You can draw a clock out to show these angles.
The three times that do create an angle less than 
, and thus are incorrect, are 2:00, 4:30, and 11:00.
2:00 has the minute hand straight up on the 12 and the hour hand straight at the 2, making it less than the 
angle created by 3:00.
4:30 has the hour hand in between the 4 and 5 and the minute hand on the 6, making it less than the 
angle created by 3:30.
11:00 has the minute hand straight up on the 12 and the hour hand straight at the 11, making it less than the 
angle created by 9:00.
1:30 is the angle that is NOT less than 
. The hour hand is in between the 1 and 2, and the minute hand is straight down on the 6. This angle is larger than a perfect right angle of 
. Therefore, 1:30 is the correct answer.
In this problem, you are working with the shape of a clock. A clock is in the shape of a circle, which has
First, it's helpful to recognize at what times a right angle (
The three times that do create an angle less than
2:00 has the minute hand straight up on the 12 and the hour hand straight at the 2, making it less than the
4:30 has the hour hand in between the 4 and 5 and the minute hand on the 6, making it less than the
11:00 has the minute hand straight up on the 12 and the hour hand straight at the 11, making it less than the
1:30 is the angle that is NOT less than
Compare your answer with the correct one above
How many degrees are in an angle formed by the hour and minute hand when it is 5:15?
How many degrees are in an angle formed by the hour and minute hand when it is 5:15?
When it is 5:15, the hour hand is pointed to 5 and the minute hand is pointed to 3.
Therefore, the angle created will span between 3 and 5, which spans "2 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to 
of the total degrees in the clock.
Since the clock is a circle, it contains 360 degrees.
of 360 is 60; therefore, 60 is the correct answer.
When it is 5:15, the hour hand is pointed to 5 and the minute hand is pointed to 3.
Therefore, the angle created will span between 3 and 5, which spans "2 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to
Since the clock is a circle, it contains 360 degrees.
Compare your answer with the correct one above
How many degrees are are in the angle formed by the minute and hour hand when it is 7:05?
How many degrees are are in the angle formed by the minute and hour hand when it is 7:05?
When it is 7:05, the hour hand is pointed to 7 and the minute hand is pointed to 1.
Therefore, the angle created will span between 1 and 7, which spans "6 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to 
of the total degrees in the clock.
Since the clock is a circle, it contains 360 degrees.
of 360 is 180; therefore, 180 is the correct answer.
When it is 7:05, the hour hand is pointed to 7 and the minute hand is pointed to 1.
Therefore, the angle created will span between 1 and 7, which spans "6 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to
Since the clock is a circle, it contains 360 degrees.
Compare your answer with the correct one above
The hour hand and the minute hand of a clock form a 30-degree angle. If the minute hand reads 55 minutes, what number may the hour hand be pointed to?
The hour hand and the minute hand of a clock form a 30-degree angle. If the minute hand reads 55 minutes, what number may the hour hand be pointed to?
When the minute hand is pointed to 55 minutes (or the 11th hour), the hour hand must be pointed to either 10 or 12.
This is because the angle created will span between 10 and 11 or 11 and 12, which spans "1 hour" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to 
of the total degrees in the clock.
Since the clock is a circle, it contains 360 degrees.
of 360 is 30; therefore, the answer choice 10 or 12 proves to be correct.
When the minute hand is pointed to 55 minutes (or the 11th hour), the hour hand must be pointed to either 10 or 12.
This is because the angle created will span between 10 and 11 or 11 and 12, which spans "1 hour" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to
Since the clock is a circle, it contains 360 degrees.
Compare your answer with the correct one above
The hour hand and the minute hand of a clock form a 60-degree angle. If the minute hand reads 45 minutes, what number may the hour hand be pointed to?
The hour hand and the minute hand of a clock form a 60-degree angle. If the minute hand reads 45 minutes, what number may the hour hand be pointed to?
When the hour hand is pointed to 45 minutes (or the 9th hour), the hour hand must be pointed to either 7 or 11.
This is because the angle created will span between 9 and 11 or 9 and 7, which spans "2 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to 
of the total degrees in the clock.
Since the clock is a circle, it contains 360 degrees.
of 360 is 60; therefore, the answer choice 7 or 11 proves to be correct.
When the hour hand is pointed to 45 minutes (or the 9th hour), the hour hand must be pointed to either 7 or 11.
This is because the angle created will span between 9 and 11 or 9 and 7, which spans "2 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to
Since the clock is a circle, it contains 360 degrees.
Compare your answer with the correct one above
The clock in the classroom reads 5:00pm. What is the angle that the hands are forming?
The clock in the classroom reads 5:00pm. What is the angle that the hands are forming?
Since the clock is a circle, you can determine that the total number of degrees inside the circle is 360. Since a clock has 12 numbers, we can divide 360 by 12 to see what the angle is between two numbers that are right next to each other. Thus, we can see that the angle between two numbers right next to each other is . However, the clock is reading 5:00, so there are five numbers we have to take in to account. Therefore, we multiply 30 by 5, which gives us as our answer.
Since the clock is a circle, you can determine that the total number of degrees inside the circle is 360. Since a clock has 12 numbers, we can divide 360 by 12 to see what the angle is between two numbers that are right next to each other. Thus, we can see that the angle between two numbers right next to each other is
Compare your answer with the correct one above
The time on a clock reads 5:00. What is the measure of the central angle formed by the hands of the clock?
The time on a clock reads 5:00. What is the measure of the central angle formed by the hands of the clock?
First, remember that the number of degrees in a circle is 360. Then, figure out how many degrees are in between each number on the face of the clock. Since there are 12 numbers, there are between each number. Since the time reads 5:00, multiply , which yields .
First, remember that the number of degrees in a circle is 360. Then, figure out how many degrees are in between each number on the face of the clock. Since there are 12 numbers, there are
Compare your answer with the correct one above
At which of the following times on a clock is the smaller angle created by the minute hand and hour hand NOT less than ?
At which of the following times on a clock is the smaller angle created by the minute hand and hour hand NOT less than
In this problem, you are working with the shape of a clock. A clock is in the shape of a circle, which has total. You are looking for the time for which the smaller angle created by the minute and hour hands is NOT less than - in other words, the time must create an angle greater than .
First, it's helpful to recognize at what times a right angle () exists. This would be 3:00 and 9:00. It's also useful to recognize that times such as 3:30 and 9:30 will be slightly under - the hour hand moves just past the 3 and 9 on a clock at these times to create this effect. You can draw a clock out to show these angles.
The three times that do create an angle less than , and thus are incorrect, are 2:00, 4:30, and 11:00.
2:00 has the minute hand straight up on the 12 and the hour hand straight at the 2, making it less than the angle created by 3:00.
4:30 has the hour hand in between the 4 and 5 and the minute hand on the 6, making it less than the angle created by 3:30.
11:00 has the minute hand straight up on the 12 and the hour hand straight at the 11, making it less than the angle created by 9:00.
1:30 is the angle that is NOT less than . The hour hand is in between the 1 and 2, and the minute hand is straight down on the 6. This angle is larger than a perfect right angle of . Therefore, 1:30 is the correct answer.
In this problem, you are working with the shape of a clock. A clock is in the shape of a circle, which has
First, it's helpful to recognize at what times a right angle (
The three times that do create an angle less than
2:00 has the minute hand straight up on the 12 and the hour hand straight at the 2, making it less than the
4:30 has the hour hand in between the 4 and 5 and the minute hand on the 6, making it less than the
11:00 has the minute hand straight up on the 12 and the hour hand straight at the 11, making it less than the
1:30 is the angle that is NOT less than
Compare your answer with the correct one above
How many degrees are in an angle formed by the hour and minute hand when it is 5:15?
How many degrees are in an angle formed by the hour and minute hand when it is 5:15?
When it is 5:15, the hour hand is pointed to 5 and the minute hand is pointed to 3.
Therefore, the angle created will span between 3 and 5, which spans "2 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to of the total degrees in the clock.
Since the clock is a circle, it contains 360 degrees.
of 360 is 60; therefore, 60 is the correct answer.
When it is 5:15, the hour hand is pointed to 5 and the minute hand is pointed to 3.
Therefore, the angle created will span between 3 and 5, which spans "2 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to
Since the clock is a circle, it contains 360 degrees.
Compare your answer with the correct one above
How many degrees are are in the angle formed by the minute and hour hand when it is 7:05?
How many degrees are are in the angle formed by the minute and hour hand when it is 7:05?
When it is 7:05, the hour hand is pointed to 7 and the minute hand is pointed to 1.
Therefore, the angle created will span between 1 and 7, which spans "6 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to of the total degrees in the clock.
Since the clock is a circle, it contains 360 degrees.
of 360 is 180; therefore, 180 is the correct answer.
When it is 7:05, the hour hand is pointed to 7 and the minute hand is pointed to 1.
Therefore, the angle created will span between 1 and 7, which spans "6 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to
Since the clock is a circle, it contains 360 degrees.
Compare your answer with the correct one above
The hour hand and the minute hand of a clock form a 30-degree angle. If the minute hand reads 55 minutes, what number may the hour hand be pointed to?
The hour hand and the minute hand of a clock form a 30-degree angle. If the minute hand reads 55 minutes, what number may the hour hand be pointed to?
When the minute hand is pointed to 55 minutes (or the 11th hour), the hour hand must be pointed to either 10 or 12.
This is because the angle created will span between 10 and 11 or 11 and 12, which spans "1 hour" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to of the total degrees in the clock.
Since the clock is a circle, it contains 360 degrees.
of 360 is 30; therefore, the answer choice 10 or 12 proves to be correct.
When the minute hand is pointed to 55 minutes (or the 11th hour), the hour hand must be pointed to either 10 or 12.
This is because the angle created will span between 10 and 11 or 11 and 12, which spans "1 hour" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to
Since the clock is a circle, it contains 360 degrees.
Compare your answer with the correct one above
The hour hand and the minute hand of a clock form a 60-degree angle. If the minute hand reads 45 minutes, what number may the hour hand be pointed to?
The hour hand and the minute hand of a clock form a 60-degree angle. If the minute hand reads 45 minutes, what number may the hour hand be pointed to?
When the hour hand is pointed to 45 minutes (or the 9th hour), the hour hand must be pointed to either 7 or 11.
This is because the angle created will span between 9 and 11 or 9 and 7, which spans "2 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to of the total degrees in the clock.
Since the clock is a circle, it contains 360 degrees.
of 360 is 60; therefore, the answer choice 7 or 11 proves to be correct.
When the hour hand is pointed to 45 minutes (or the 9th hour), the hour hand must be pointed to either 7 or 11.
This is because the angle created will span between 9 and 11 or 9 and 7, which spans "2 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to
Since the clock is a circle, it contains 360 degrees.
Compare your answer with the correct one above
The clock in the classroom reads 5:00pm. What is the angle that the hands are forming?
The clock in the classroom reads 5:00pm. What is the angle that the hands are forming?
Since the clock is a circle, you can determine that the total number of degrees inside the circle is 360. Since a clock has 12 numbers, we can divide 360 by 12 to see what the angle is between two numbers that are right next to each other. Thus, we can see that the angle between two numbers right next to each other is . However, the clock is reading 5:00, so there are five numbers we have to take in to account. Therefore, we multiply 30 by 5, which gives us as our answer.
Since the clock is a circle, you can determine that the total number of degrees inside the circle is 360. Since a clock has 12 numbers, we can divide 360 by 12 to see what the angle is between two numbers that are right next to each other. Thus, we can see that the angle between two numbers right next to each other is
Compare your answer with the correct one above
The time on a clock reads 5:00. What is the measure of the central angle formed by the hands of the clock?
The time on a clock reads 5:00. What is the measure of the central angle formed by the hands of the clock?
First, remember that the number of degrees in a circle is 360. Then, figure out how many degrees are in between each number on the face of the clock. Since there are 12 numbers, there are between each number. Since the time reads 5:00, multiply , which yields .
First, remember that the number of degrees in a circle is 360. Then, figure out how many degrees are in between each number on the face of the clock. Since there are 12 numbers, there are
Compare your answer with the correct one above
At which of the following times on a clock is the smaller angle created by the minute hand and hour hand NOT less than ?
At which of the following times on a clock is the smaller angle created by the minute hand and hour hand NOT less than
In this problem, you are working with the shape of a clock. A clock is in the shape of a circle, which has total. You are looking for the time for which the smaller angle created by the minute and hour hands is NOT less than - in other words, the time must create an angle greater than .
First, it's helpful to recognize at what times a right angle () exists. This would be 3:00 and 9:00. It's also useful to recognize that times such as 3:30 and 9:30 will be slightly under - the hour hand moves just past the 3 and 9 on a clock at these times to create this effect. You can draw a clock out to show these angles.
The three times that do create an angle less than , and thus are incorrect, are 2:00, 4:30, and 11:00.
2:00 has the minute hand straight up on the 12 and the hour hand straight at the 2, making it less than the angle created by 3:00.
4:30 has the hour hand in between the 4 and 5 and the minute hand on the 6, making it less than the angle created by 3:30.
11:00 has the minute hand straight up on the 12 and the hour hand straight at the 11, making it less than the angle created by 9:00.
1:30 is the angle that is NOT less than . The hour hand is in between the 1 and 2, and the minute hand is straight down on the 6. This angle is larger than a perfect right angle of . Therefore, 1:30 is the correct answer.
In this problem, you are working with the shape of a clock. A clock is in the shape of a circle, which has
First, it's helpful to recognize at what times a right angle (
The three times that do create an angle less than
2:00 has the minute hand straight up on the 12 and the hour hand straight at the 2, making it less than the
4:30 has the hour hand in between the 4 and 5 and the minute hand on the 6, making it less than the
11:00 has the minute hand straight up on the 12 and the hour hand straight at the 11, making it less than the
1:30 is the angle that is NOT less than
Compare your answer with the correct one above
How many degrees are in an angle formed by the hour and minute hand when it is 5:15?
How many degrees are in an angle formed by the hour and minute hand when it is 5:15?
When it is 5:15, the hour hand is pointed to 5 and the minute hand is pointed to 3.
Therefore, the angle created will span between 3 and 5, which spans "2 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to of the total degrees in the clock.
Since the clock is a circle, it contains 360 degrees.
of 360 is 60; therefore, 60 is the correct answer.
When it is 5:15, the hour hand is pointed to 5 and the minute hand is pointed to 3.
Therefore, the angle created will span between 3 and 5, which spans "2 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to
Since the clock is a circle, it contains 360 degrees.
Compare your answer with the correct one above
How many degrees are are in the angle formed by the minute and hour hand when it is 7:05?
How many degrees are are in the angle formed by the minute and hour hand when it is 7:05?
When it is 7:05, the hour hand is pointed to 7 and the minute hand is pointed to 1.
Therefore, the angle created will span between 1 and 7, which spans "6 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to of the total degrees in the clock.
Since the clock is a circle, it contains 360 degrees.
of 360 is 180; therefore, 180 is the correct answer.
When it is 7:05, the hour hand is pointed to 7 and the minute hand is pointed to 1.
Therefore, the angle created will span between 1 and 7, which spans "6 hours" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to
Since the clock is a circle, it contains 360 degrees.
Compare your answer with the correct one above
The hour hand and the minute hand of a clock form a 30-degree angle. If the minute hand reads 55 minutes, what number may the hour hand be pointed to?
The hour hand and the minute hand of a clock form a 30-degree angle. If the minute hand reads 55 minutes, what number may the hour hand be pointed to?
When the minute hand is pointed to 55 minutes (or the 11th hour), the hour hand must be pointed to either 10 or 12.
This is because the angle created will span between 10 and 11 or 11 and 12, which spans "1 hour" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to of the total degrees in the clock.
Since the clock is a circle, it contains 360 degrees.
of 360 is 30; therefore, the answer choice 10 or 12 proves to be correct.
When the minute hand is pointed to 55 minutes (or the 11th hour), the hour hand must be pointed to either 10 or 12.
This is because the angle created will span between 10 and 11 or 11 and 12, which spans "1 hour" worth of time on the clock. Given that there are a total of 12 hours of time on the clock, this means that the angle formed will be equal to
Since the clock is a circle, it contains 360 degrees.
Compare your answer with the correct one above