A clock face has the numbers 1 through 12 Each number is 1/12 of a complete circle which is 360 degrees.
Each number is 360 / 12 = 30 degrees
For a clock reading 12:25, the hands are on the 12 and 5
The angle would be 30 x 5 = 150 degrees.
It is larger than 90, so could be called an obtuse angle.
The angle between the minute hand and the hour hand of the clock at 12:25 is 137.5°
There are 12 hourly partitions in clock.
Full rotation is of 360°, so each of 12 partition has 360/12 = 30° angle between them.
The mark of 12 to 1 has 30° angle, the mark of 1 to 2 has 30 ° angle and so on.
In each of 12 hourly partition in clock, there are five-five minor partition .
There are therefore 12 times 5 = 60 minor partitions.
Those minor 5-5 partitions have 30/5 = 6° angle between them.
As minute hand moves one full circle, one hour happens. And the hourly hand moves 5 minor partition (30°)
That means, as the minute hand moves by 360° by 1 rotation, the hour hand moves by 30°.
Suppose the time is 12:00 when all hands of the clock are on the 12 mark. Now,
at 12:25, the minute hand is on 25, which is 5 time 5 minor partition = 5 times 30 = 150° from the 12 mark.
Since as 360° motion of minute hand, the hour hand moves by 30°, so when the hour hand moves 1°, then the hour hand moves by 30/360 = 1/12°.
And therefore, when hour hand moves by 150°, then the hour hand moves by:
[tex]\dfrac{1}{12} \times 150 = 12.5^\circ[/tex]
Now we know that:
At 12:25,
Thus, the angle between them is:
[tex]150-12.5 = 137.5^\circ[/tex] (smaller angle, we angle the minute hand will need to travel in clockwise way to reach hour hand's current position).
Thus, the angle between the minute hand and the hour hand of the clock at 12:25 is 137.5°
Learn more about angle between hands in a clock here:
https://brainly.com/question/1542103
