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 1: Understand the positions of the hands
At 4 o'clock:
- The hour hand is on the 4.
- The minute hand is on the 12.

### Step 2: Calculate the angle for the hour hand
The clock is divided into 12 hours, and a full circle is 360 degrees. Therefore, each hour represents an angle of:
\[ \text{Angle per hour} = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees per hour} \]
At 4 o'clock, the hour hand is at the 4th hour mark:
\[ \text{Angle of hour hand} = 4 \times 30 = 120 \text{ degrees} \]

### Step 3: Calculate the angle for the minute hand
At 4 o'clock, the minute hand is at the 12 o'clock position, which corresponds to:
\[ \text{Angle of minute hand} = 0 \text{ degrees} \]

### Step 4: Find the angle between the hour and minute hands
To find the angle between the hour and minute hands, we subtract the angle of the minute hand from the angle of the hour hand:
\[ \text{Angle between hands} = \text{Angle of hour hand} - \text{Angle of minute hand} = 120 \text{ degrees} - 0 \text{ degrees} = 120 \text{ degrees} \]

### Final Answer
Thus, when a clock shows 4 o'clock, the angle between the minute and hour hands is **120 degrees**.

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