sat Math assist » Geometry » aircraft Geometry » one » Clock math » exactly how to find the angle of clock hands

Explanation:

At 4 o’clock the minute hand is top top the 12 and also the hour hand is on the 4. The angle created is 4/12 of the total variety of degrees in a circle, 360.

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4/12 * 360 = 120 degrees

Explanation:

A clock is a circle, and also a circle always contains 360 degrees. Because there space 60 minute on a clock, every minute mark is 6 degrees.

The minute hand ~ above the clock will allude at 15 minutes, permitting us to calculation it"s place on the circle.

Since there are 12 hours on the clock, each hour note is 30 degrees.

We deserve to calculate whereby the hour hand will be in ~ 8:00.

However, the hour hand will certainly actually be between the 8 and the 9, since we are looking in ~ 8:15 rather than an pure hour mark. 15 minutes is same to one-fourth of an hour. Usage the very same equation to uncover the additional position the the hour hand.

We are in search of the angle in between the two hands the the clock. The will be equal to the difference between the two angle measures.

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### Example concern #1 : exactly how To find The angle Of Clock hands

What is the measure of the smaller angle developed by the hands of an analog clock if the hour hand is top top the 10 and the minute hand is top top the 2?

90°

56°

45°

120°

30°

120°

Explanation:

A analog clock is separated up right into 12 sectors, based on the number 1–12. One sector represents 30 levels (360/12 = 30). If the hour hand is directly on the 10, and also the minute hand is top top the 2, that method there are 4 sectors the 30 degrees between then, thus they room 120 levels apart (30 * 4 = 120).

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### Example question #2 : exactly how To uncover The angle Of Clock hands

At

, what angle is between the hour and also minute hand on a clock?

Explanation:

At

, the hour hand is ~ above the
and the minute hand is in ~ the
. There room
spaces on a clock, and also these hands space separated by
spaces.

Thus, the angle in between them is

the levels of the whole clcok, i m sorry is
.

Therefore, us multiply these to obtain our answer.

We have the right to cancel out as we multiply to get:

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### Example concern #1 : how To uncover The angle Of Clock hands

What is the measure, in degrees, of the acute angle formed by the hand of a 12-hour clock that reads exactly 3:10?

55°

60°

72°

35°

65°

35°

Explanation:

The whole clock procedures 360°. As the clock is split into 12 sections, the distance in between each number is tantamount to 30° (360/12). The distance between the 2 and also the 3 ~ above the clock is 30°. One needs to account, however, because that the 10 minutes that have actually passed. 10 minute is 1/6 of one hour therefore the hour hand has likewise moved 1/6 the the distance between the 3 and also the 4, which add to 5° (1/6 that 30°). The complete measure of the angle, therefore, is 35°.

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### Example concern #3 : how To uncover The angle Of Clock hands

If it is 4:00, what is the measure of the angle in between the minute and hour hands of the clock?

100 degrees

125 degrees

90 degrees

120 degrees

45 degrees

120 degrees

Explanation:

A clock take away the form of a circle, i beg your pardon is composed of 360 degrees. There are 12 numbers on a clock that represent the hours. V this in mind, we have the right to say that each number represents an angle. The measure of the angle in between each number is provided by

.

If that is 4:00, then the minute hand is pointing towards 12 if the hour hand points towards 4.

Therefore, we have the right to say that the angle between the two hands is

degrees.

Another means to think the this is come imagine the clock in ~ a nearby time. At 3:00, the hand of the clock form a appropriate angle that 90 degrees. Because we understand that every number top top the clock is be separate by 30 degrees, we have the right to simply add 30 come 90 degrees and get 120 levels for the angle at 4:00.

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### Example question #4 : exactly how To discover The angle Of Clock hand

If the is 2:00 PM, what is the measure of the angle between the minute and hour hand of the clock?

90 degrees

60 degrees

30 degrees

45 degrees

120 degrees

60 degrees

Explanation:

First note that a clock is a circle make of 360 degrees, and that every number to represent an angle and the separation in between them is 360/12 = 30. And also at 2:00, the minute hand is top top the 12 and also the hour hand is on the 2. The exactly answer is 2 * 30 = 60 degrees.

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