Question

At which other time is the angle between the hands congruent with this hand?​

Answer 1

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

Answer:

The correct answer is 4:45

Explanation:

First of all we have to measure the angle between two consecutive numbers in a clock:

360°/12=30°

Now, let us assume that number 12 in clock as our zero degree point

Now we know the congruent angles will be made at 4:45 and at the 4:45, the minute hand will be at the number 9 of clock means it will cover the angle of:

30°×9=270°

And, the hour hand will be 3/4th distance far from the number 4 on the clock means it will cover the angle of:

30°×4.75=142.5°

Now the congruent angles made by the hands will be:

(angle covered by minute hand - angle covered by hour hand)

270° - 142.5° = 127.5°