sat Math help » Geometry » aircraft Geometry » circles » Clock mathematics » just how to uncover the angle of clock hands

Explanation:

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

You are watching: It’s 2 pm. how many degrees are in the angle between the hour and minute hand?

4/12 * 360 = 120 degrees

Explanation:

A clock is a circle, and also 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 point at 15 minutes, allowing us to calculation it"s place on the circle.

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

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

However, the hour hand will certainly actually be between the 8 and also the 9, since we are looking at 8:15 quite than an absolute hour mark. 15 minute is same to one-fourth of one hour. Usage the same equation to discover the added position the the hour hand.

We are trying to find the angle in between the two hands that the clock. The will be equal to the difference in between the 2 angle measures.

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Example question #1 : how To uncover The edge Of Clock hand

What is the measure of the smaller angle developed by the hands of one analog watch if the hour hand is ~ above the 10 and also 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 degrees (360/12 = 30). If the hour hand is directly on the 10, and also the minute hand is ~ above the 2, that method there room 4 sectors of 30 degrees between then, hence they are 120 degrees apart (30 * 4 = 120).

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Example concern #2 : exactly how To find The edge Of Clock hand

At

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

Explanation:

At

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

Thus, the angle in between them is

the degrees of the entire clcok, which is
.

Therefore, us multiply these to get our answer.

We deserve to cancel out together we multiply to get:

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Example concern #8 : just how To uncover The angle Of Clock hands

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

35°

65°

55°

60°

72°

35°

Explanation:

The whole clock actions 360°. Together the clock is split 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, because that the 10 minutes that have actually passed. 10 minute is 1/6 of an hour therefore the hour hand has also moved 1/6 the the distance in between the 3 and the 4, which to add 5° (1/6 of 30°). The complete measure that the angle, therefore, is 35°.

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Example inquiry #3 : exactly how To discover The angle Of Clock hand

If the is 4:00, what is the measure up of the angle between the minute and also hour hand of the clock?

100 degrees

125 degrees

90 degrees

120 degrees

45 degrees

120 degrees

Explanation:

A clock bring away the form of a circle, which is written of 360 degrees. There space 12 numbers on a clock that stand for the hours. With this in mind, we can say the each number to represent an angle. The measure up of the angle between each number is provided by

.

See more: How Many Ounces Is 400 Ml To Oz, 400 Ml To Oz

If it is 4:00, then the minute hand is pointing in the direction of 12 while the hour hand points towards 4.

Therefore, we deserve to say that the angle between the 2 hands is

degrees.

Another way to think of this is come imagine the clock in ~ a adjacent time. At 3:00, the hand of the clock form a best angle of 90 degrees. Because we understand that each number ~ above 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 edge at 4:00.

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Example concern #4 : how To uncover The edge Of Clock hands

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

90 degrees

60 degrees

30 degrees

45 degrees

120 degrees

60 degrees

Explanation:

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

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