Question

How far does a minute hand go from 12, if it makes an angle of 270 degree ?

Answer 1

Answer:

Explanation:

The angle measure between any two consecutive numbers on a clock is 36012=30∘.

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

At 4:45, the minute hand is at the "9" - that is, at the 30×9=270∘ mark. The hour hand is three-fourths of the way from the "4" to the "5; that is,

30×434=142.5∘ mark.

Therefore, the angle between the hands is

270−142.5=127.5∘, the desired measure.

Answer 2

If the minute hand makes an angle of 270 degrees, it moves a quarter of the way around the clock face, or 90 degrees.

A minute hand makes one full rotation, 360 degrees, in 60 minutes, so in one minute it moves 360 degrees / 60 minutes = 6 degrees.

Therefore, in 90 minutes, the minute hand moves 90 minutes * 6 degrees/minute = 540 degrees.

So the minute hand moves from 12 to the position that is 540 degrees clockwise from 12, which is the 6 o'clock position.