Question

What is the angle between the two hands of a clock, when the time is 9 hours 10 minutes?

180°
145°
120°
225°​

Answer 1

Explanation:

For any clock time X:Y (substituting 0 for the hour when the hour is 12, and using 0 degrees for straight up pointing to the 12):

The angle of the minute hand (Y) from 12 will be given by 6Y degrees.

The angle of the hour hand (X) from 12 will be given by (30X + 0.5Y) degrees.

a(X) = 30X + 0.5Y degrees

a(Y) = 6y degrees

Now we can use these formulas to determine the clock time for any angle formed between two hands. For the angle at time 9:10,

X = 9

Y = 10

a(X) = 30X + 0.5Y = 270 + 5 = 275 degrees

a(Y) = 6Y = 60 degrees

The difference between these 2 angles = the angle formed between the 2 hands going clockwise from minute hand to hour hand:

275 - 60 = 215 degrees between the hands at clock time 9:10

For the angle going clockwise from hour hand to minute hand, subtract 215 from 360 degrees to obtain:

360 - 215 = 145 degrees between the hands at clock time 9:10