Question

When the time in the clock is 12.20,then the angle between the hands of the clock is x degree. find the value of x degree?

Answer 1

We know that,

In a clock,
Angle described by minute hand in 1 min = 6°

Angle described by minute hand in 20 min = 6* 20 = 120°

So, required answer is x = 120°

Answer 2

Given,

The time on the clock is 12.20.

The angle between the hands of the clock is x degrees.

To find,

Value of x.

Solution,

This problem can be simply solved by following the below steps.

Firstly, let's understand how the angles of the hour hand and minute hand are measured or determined.

As we know that the hour hand completes one revolution about the center in 12 hours. So, it makes 360° in 12 hours. It means the angle made by hour hand in one hour or 60 minutes, will be 360/12, that is 30°. To find out the angle by which the hour hand is rotated in 1 minute, we need to divide 30 by 60, that is, 30/60 = 0.5.

It means the hour hand rotates by just 0.5° in 1 minute.

Now, for the minute hand, we can see that it completes a revolution about the center in 60 minutes. So, in one minute, the angle by which the minute hand turns is 360/60 = 6.

It means the minute hand turns by 6° in 1 minute.

Now, to find out the angle between the hour hand and minute hand at a given time, we can subtract the angle made by the hour hand from the angle made by the minute hand, at that time.

Now, the angle by which the hour hand rotates in 20 minutes will be,

0.5*20 = 10°.

The angle by which the minute hand turns in 20 minutes,

6*20 = 120°.

The angle between both the hands is given as x, so x will be

x = 120 - 10 = 110°.

Therefore, for the time on the clock 12.20, the value of x will be 110°.