Question

What is the degree measure of the smaller angle formed by the hour and minute hands of a 12 hour clock?

Answer 1

359.905 degrees is the answer.

Step-by-step explanation:

when it comes to the hour hand it moves about 360 degrees in a 12 hour clock for instance let us take the time 6:15 then the calculation is

=(6+15/60) * 360÷12

= 187.5 degrees.

when it comes to the minute hand the minute hand travels 360 degrees for every 60 minutes in a 12 hour clock so if it is 5 mins past in the time 6:05 then it can be given as

15/60 * 360 = 90 degrees

Difference between the two hand can be  calculated by

(Angle turned by the hour hand) - (Angle turned by the minute hand)

For a smaller angle let us take 12:01

= (12+1/60) * 360÷12

=360.5

for the minute hand

=1/60 = 0.595

(Angle turned by the hour hand) - (Angle turned by the minute hand)

= 360.5 - 0.595

= 359.905 degrees