Answer:

7:20

The angle between the hands at 7:20 is, therefore, [(3* 30 degrees) + (1/3 * 30 degrees)] = [(90 degrees) + (10 degrees)] = 100 degrees

2:10

Hence, the angle between the hour and minute hands of a clock when it strikes 2:10 pm will be 5 degrees

12:12

To find this minor movement of the hour hand, let’s convert the 12 minutes traveled by the minute hand into a portion of an hour:

(12 minutes / 60 minutes/hour) * (30 degrees/hour) = 6 degrees

4:20

Thus, angle between two hands = 130−120=10∘

9:15

Again, the two angles created by the hour hand and minute hand at nine-fifteen are 172.5 degrees and 187.5 degrees

Step-by-step explanation:

To find the angle for each time in the given format (hour:minute), you can use the following formula:

\[ \text{Angle} = \left| 30H - \frac{11}{2}M \right| \]

where:

- \( H \) is the hour,

- \( M \) is the minute.

Now, let's calculate for each case:

a) For 7:20:

\[ \text{Angle} = \left| 30 \times 7 - \frac{11}{2} \times 20 \right| = \left| 210 - 110 \right| = 100 \]

b) For 2:10:

\[ \text{Angle} = \left| 30 \times 2 - \frac{11}{2} \times 10 \right| = \left| 60 - 55 \right| = 5 \]

c) For 12:12:

\[ \text{Angle} = \left| 30 \times 12 - \frac{11}{2} \times 12 \right| = \left| 360 - 66 \right| = 294 \]

d) For 4:20:

\[ \text{Angle} = \left| 30 \times 4 - \frac{11}{2} \times 20 \right| = \left| 120 - 110 \right| = 10 \]

e) For 9:15:

\[ \text{Angle} = \left| 30 \times 9 - \frac{11}{2} \times 15 \right| = \left| 270 - 82.5 \right| = 187.5 \]

Therefore, the angles are:

a) 100 degrees

b) 5 degrees

c) 294 degrees

d) 10 degrees

e) 187.5 degrees