When a clock shows `4` o' clock how much angle do its minute and hour needles make?

Options

A. `120^(@)`
B. `pi/3 rad`
C. `(2pi)/3 rad`
D. `160^(@)`

Explanation

To find the angle between the hour and minute hands of a clock when it shows 4 o'clock, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Clock Division**:
A clock is divided into 12 hours, and the total angle of a clock is 360 degrees.

2. **Calculate the Angle Between Hour Marks**:
The angle between any two consecutive hour marks can be calculated as:
\[ \text{Angle between hour marks} = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees} \]

3. **Identify the Hour Mark**:
At 4 o'clock, the hour hand points at the 4 mark.

4. **Count the Hour Marks**:
The number of hour marks between the hour hand (4) and the 12 o'clock position (where the minute hand points at 0) is 4.

5. **Calculate the Total Angle**:
To find the total angle between the hour and minute hands, multiply the angle between the hour marks by the number of hour marks:
\[ \text{Total angle} = \text{Angle between hour marks} \times \text{Number of hour marks} = 30 \text{ degrees} \times 4 = 120 \text{ degrees} \]

6. **Conclusion**:
Therefore, the angle between the minute and hour hands when the clock shows 4 o'clock is 120 degrees.

### Final Answer:
The angle between the minute and hour hands at 4 o'clock is **120 degrees**.

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