At four o’clock the minute hand is on the 12 and also the hour hand is on the 4. The angle formed is 4/12 the the total number of degrees in a circle, 360.
You are watching: Find the measure of the smaller angle formed by the hands of a clock
4/12 * 360 = 120 degrees
A clock is a circle, and a circle always contains 360 degrees. Due to the fact that there space 60 minute on a clock, each minute mark is 6 degrees.
The minute hand ~ above the clock will allude at 15 minutes, enabling us to calculation it"s position on the circle.
Since there room 12 hrs on the clock, every hour note is 30 degrees.
We deserve to calculate where the hour hand will certainly be in ~ 8:00.
However, the hour hand will actually it is in between the 8 and also the 9, since we room looking in ~ 8:15 quite than an pure hour mark. 15 minutes is equal to one-fourth of an hour. Usage the same equation to discover the extr position that the hour hand.
We are searching for the angle between the 2 hands the the clock. The will certainly be same to the difference in between the 2 angle measures.
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Example inquiry #1 : exactly how To uncover The edge Of Clock hand
What is the measure up of the smaller angle formed by the hand of one analog clock if the hour hand is ~ above the 10 and also the minute hand is on the 2?
A analog clock is divided up into 12 sectors, based on the numbers 1–12. One sector represents 30 levels (360/12 = 30). If the hour hand is straight on the 10, and also the minute hand is top top the 2, that means there space 4 sectors of 30 degrees in between then, hence they are 120 levels apart (30 * 4 = 120).
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Example concern #2 : how To discover The edge Of Clock hands
Thus, the angle between them is
Therefore, we multiply this to get our answer.
We deserve to cancel out together we multiply to get:
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Example inquiry #1 : just how To uncover The angle Of Clock hand
What is the measure, in degrees, of the acute angle developed by the hand of a 12-hour clock the reads precisely 3:10?
The whole clock procedures 360°. Together the clock is separated 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 minute that have passed. 10 minute is 1/6 of one hour for this reason the hour hand has likewise moved 1/6 that the distance in between the 3 and the 4, which add to 5° (1/6 that 30°). The complete measure the the angle, therefore, is 35°.
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Example inquiry #3 : how To uncover The edge Of Clock hands
If that is 4:00, what is the measure of the angle between the minute and also hour hands of the clock?
A clock takes the shape of a circle, i beg your pardon is composed of 360 degrees. There are 12 numbers on a clock that represent the hours. Through this in mind, we deserve to say the each number to represent an angle. The measure of the angle in between each number is given by
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If the is 4:00, climate the minute hand is pointing in the direction of 12 if the hour hand points in the direction of 4.
Therefore, we can say the the angle between the two hands is
Another way to think the this is come imagine the clock at a surrounding time. In ~ 3:00, the hand of the clock form a right angle of 90 degrees. Since we understand that each number top top the clock is be separated by 30 degrees, we deserve to simply add 30 to 90 degrees and also get 120 levels for the edge at 4:00.
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Example inquiry #4 : just how To discover The angle Of Clock hands
If it is 2:00 PM, what is the measure up of the angle between the minute and hour hands of the clock?
First note that a clock is a circle made of 360 degrees, and also that each number represents an angle and the separation in between them is 360/12 = 30. And at 2:00, the minute hand is on the 12 and the hour hand is ~ above the 2. The correct answer is 2 * 30 = 60 degrees.
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