High institution Math assist » Geometry » aircraft Geometry » circles » Clock mathematics » just how to discover the edge of clock hands     Explanation:

The distance between each notch on the clock is 6 degrees since there room 360 levels on the clock, and also there are 60 notches total. The minute hand is in ~ notch #20, and also so it is 120 levels from the top. The hour hand is a tiny past notch #40 due to the fact that the time is a small past hour 8. Thus, the hour hand is a tiny past 240 degrees from the top, walking clockwise ( degrees).

You are watching: Find the measure of the smaller angle formed by the hands of a clock at the following time.

In each hour, the hour hand walk 5 notches, or 30 degrees. Since it is now 20 minutes past the hour, a 3rd of one hour has passed. One third of 30 levels is 10 degrees. Thus, the hour hand is 10 degrees past notch #40. The hour hand is 250 degrees from the top, walking clockwise. The angle in between the two hands is thus 130 degrees.

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### Example concern #2 : exactly how To uncover The angle Of Clock hand

When making a pie chart, how numerous degrees should be allotted for percent? Explanation:

This is a ratio problem so there are in percent of a circle

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

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

60 degrees

45 degrees

120 degrees

90 degrees

30 degrees

60 degrees

Explanation:

First keep in mind that a clock is a circle do of 360 degrees, and that each number represents an angle and also the separation 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 correct answer is 2 * 30 = 60 degrees.

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### Example concern #4 : how To discover The angle Of Clock hands

A clock at this time reads 2:00. What is the dimension of the edge formed in between the hour and also minute hands? Explanation:

The interior angle of a ar is same the the angle of the sector. If the whole circumference to be the sector, it would equal . Additionally, if it to be 12:00, the angle would certainly be equal to . We have the right to solve the problem by setting up a proportion. 2:00 will be two-twelfths of the circle previous the 12:00 mark, and will be at an edge of . Cross multiply and solve for .  Report one Error

### Example concern #1 : how To discover The edge Of Clock hand

It is 4 o’clock. What is the measure of the angle formed in between the hour hand and also the minute hand? Explanation:

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

4/12 * 360 = 120 degrees

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### Example concern #5 : how To find The angle Of Clock hand

If a clock reads 8:15 PM, what angle do the hands make? Explanation:

A clock is a circle, and also a circle constantly contains 360 degrees. Because there space 60 minutes on a clock, each minute note is 6 degrees. The minute hand top top the clock will suggest at 15 minutes, permitting us to calculation it"s position on the circle. Since there space 12 hours on the clock, every hour note is 30 degrees. We have the right to calculate wherein the hour hand will be at 8:00. However, the hour hand will actually be between the 8 and also the 9, due to the fact that we space looking at 8:15 quite than an pure hour mark. 15 minute is same to one-fourth of one hour. Use the same equation to discover the extr position that the hour hand.   We are in search of the angle in between the 2 hands that the clock. The will be equal to the difference in between the 2 angle measures. Report one Error

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

What is the measure up of the smaller angle developed by the hand of one analog watch if the hour hand is top top the 10 and also the minute hand is ~ above the 2?

120°

90°

56°

45°

30°

120°

Explanation:

A analog clock is divided up right into 12 sectors, based on the number 1–12. One sector to represent 30 degrees (360/12 = 30). If the hour hand is directly on the 10, and also the minute hand is top top the 2, that means there are 4 sectors the 30 degrees in between then, hence they space 120 levels apart (30 * 4 = 120).

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### Example concern #1 : exactly how To find The edge Of Clock hand

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

55°

72°

35°

65°

60°

35°

Explanation:

The whole clock measures 360°. Together the clock is separated into 12 sections, the distance in between each number is tantamount to 30° (360/12). The distance in between the 2 and also the 3 on the clock is 30°. One needs to account, however, for the 10 minutes that have passed. 10 minute is 1/6 of an hour so the hour hand has additionally moved 1/6 the the distance between the 3 and also the 4, which to add 5° (1/6 of 30°). The total measure the the angle, therefore, is 35°.

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