It is 1: 50pm. what is the sum of the degrees the minute and hour hands of a clock will rotate between now and when it hits 2: 15pm?

162.5°

Step-by-step explanation:

1. Calculate the number of minutes

(a) Subtract the hours and the minutes separately

2:  15

-1:  50

1: -35

(ii) If the minutes are negative, subtract 1 from the hours and add 60 to the minutes.

1:  -35

-1: +60

0:   25

The clock has been running for 25 min.

2. Calculate the travel of the minute hand (θm)

The clock face is a circle of 360°, and there are 60 min in 1 h,

so, the minute hand travels 6° in 1 min.

In 25 min, the minute hand will travel

θm = 25 × 6 = 150°

3. Calculate the travel of the hour hand (θh)

The hour hand travels 360° in 12 h, so it travels 30° in 1 h and 0.5° in 1 min.

It has travelled for 25 min.

θh = 25 × 0.5 = 12.5°

4. Calculate the sum of the angles

θm + θh = 150° + 12.5° = 162.5°