How many degrees is the angle between the hands of the clock if the clock shows 3 hours and 15 minutes?

In this task, we need to calculate the angle between the minute and hour hands.

This can be done in two ways.

1 way

Let’s write the ratio of 15 minutes to the time at 12 o’clock, converting hours into minutes:
15 / (12 h * 60 min) = 15/720 min = 3/144 min.

Now the angle between the minute and hour hands in degrees:
x / 360 = 3/144 ->

x = 360 * 3/144 = 1080/144 = 7.5.

2 way

Let’s calculate the fraction of 15 minutes from the whole hour:
15 min / 60 min = 1/4 h.

Let’s find how many degrees, it will be 1 hour on the dial:

360o / 12 h = 30

now we can find the angle by multiplying the degree measure of the 1st hour by the fraction that takes 15 minutes:
1/4 * 30 = 7.5.

Answer: 7.5.