basic Geometry assist » airplane Geometry » one » Clock mathematics » exactly how to uncover the angle of clock hands

Explanation:

The angle measure up between any kind of two consecutive number on a clock is

.

You are watching: What is the angle between the hands of a clock at 4 o clock

Call the "12" suggest on the clock the zero-degree point.

At 4:45, the minute hand is in ~ the "9" - the is, in ~ the

mark. The hour hand is three-fourths that the way from the "4" come the "5; that is,

Therefore, the angle between the hands is

, the preferred measure.

Explanation:

At 4:40, the minute hand is top top the 8, and also the hour hand is two-thirds that the method from the 4 come the 5. That is, the hands space three and also one-third number location apart. Each number place is thirty degrees about the clock, for this reason the hands type an edge of

.

Explanation:

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

4/12 * 360 = 120 degrees

The hour hand top top a clockface points come the

, and the minute hand points come the
. How countless degrees is the angle between the minute and hour hands?

Explanation:

There space

levels in one complete revolution of a circle. There room
minute in one hour.

Create a fraction out of this two quantities to use later on as a switch rate:

Between the

and
there space
minutes, so main point this through the conversion rate to settle for the number of degrees:

What is the measure up of the smaller angle created by the hands of an analog watch if the hour hand is ~ above the 10 and the minute hand is ~ above the 2?

Explanation:

A analog clock is divided up right into 12 sectors, based on the numbers 1–12. One sector to represent 30 degrees (360/12 = 30). If the hour hand is straight on the 10, and the minute hand is ~ above the 2, that way there are 4 sectors that 30 degrees in between then, for this reason they space 120 levels apart (30 * 4 = 120).

Thomas is trying to identify the angle in between the hand of his clock. Right currently it reads

pm, what angle execute the clock hands make?

Explanation:

You deserve to think the a clock in 2 ways:

1. Out of 12 hours, or

2. In terms of a circle through

If you try to settle it in terms of #1:

Goal: find the edge measurement in between the hour and also the minute hands. We only want to discover the degrees between the hours of 9 and also 12

So we space looking in ~ 3 hours out the the 12 total hours on a clock.

As a fraction:

So that method that the clock hands space making an angle the is 1/4 that the clock (which is a circle). So understanding that a circle has

in it,

1/4 the a one is

.

____________________________________________________________

2. If you think of the clock as a circle first you have the right to determine the angle the the clock hands create very quickly.

Since there are

in a circle, every hour that passes is a movement of
. So understanding that, the clock will be relocating 3 hours:

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### Example concern #7 : just how To find The angle Of Clock hand

What is the measure of the larger angle developed by the hands of a clock in ~

?

Explanation:

Like any type of circle, a clock includes a full of

. Due to the fact that the clock challenge is divided into
equal parts, we can discover the variety of degrees in between each number by doing
. In ~ 5:00 the hour hand will certainly be in ~ 5 and the minute hand will be at 12. Making use of what we simply figured out, we can see the there is an edge of
between the 2 hands. We are in search of the larger angle, however, so we must now do

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### Example question #1 : 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 specifically 3:10?

72°

55°

65°

35°

60°

35°

Explanation:

The entire 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 has to account, however, because that the 10 minutes that have passed. 10 minutes is 1/6 of an hour so the hour hand has also moved 1/6 that the distance between the 3 and the 4, which to add 5° (1/6 of 30°). The full measure that the angle, therefore, is 35°.

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### Example question #9 : just how To find The edge Of Clock hands

Find the angle in degrees in between clock hands at 3:30.

Explanation:

On an initial glance, this trouble may seem basic in the the angle between the 3 and 6 ~ above a clock is one 4 minutes 1 of a circle or 90 degrees. However, you should take into account that in the fifty percent hour that has actually passed from 3:00 come 3:30, the hour hand has moved fifty percent the distance between the 3 and also 4. To uncover the degrees, just divide the total variety of degrees in a circle by 12 to uncover the degrees between each continually number, and also then multiply the number by 2.5 since you have fifty percent the distance to the 4, and the the full distance come the 5 and also the complete distance to the 6. Thus,

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### Example inquiry #10 : exactly how To discover The edge Of Clock hands

A clock shows that the moment is 9:00am. What is the angle in between the minute and the hour hands?

Explanation:

By separating the clock into pieces, we have the right to determine that the angle in between the two hands is

.

See more: What Animal Drinks The Most Water ? How Can Sea Mammals Drink Saltwater

Within a clock, just like any kind of circle, there are 360 complete degrees

Within one clock, there are 60 total minutes.

Each minute that passes, the minute hand advances 6 degrees. The hour hand breakthroughs .5 degrees. But due to the fact that it is 9am on the dot, us will just be making use of the minute hand to count the degrees.

Since the minute hand is spanning a complete of 15 minute in between it and also the hour hand, we have the right to do the math:

=

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