What is the angle between the minute hand and hour hand when the clock shows 4:25 hours?

The correct option is 17.5°.

To find the angle between the hour hand and the minute hand of a clock at 4:25, we can calculate the position of each hand relative to the 12 o'clock mark (0° position) and then find the absolute difference between these two positions.

First, let's understand the movement of each hand on a standard 12-hour clock face:
A complete circle is 360°, representing 12 hours or 60 minutes.

1. Calculate the position of the hour hand:
The hour hand completes a full circle of 360° in 12 hours.
Therefore, the rate of movement of the hour hand is:
$$\frac{360°}{12\text{hours}}=30°\text{per hour}$$ Since there are 60 minutes in an hour, the hour hand also moves per minute at a rate of:
$$\frac{30°}{60\text{minutes}}=0.5°\text{per minute}$$ At 4:25, the hour hand has been moving for 4 hours and 25 minutes.
Total angle moved by the hour hand from the 12 o'clock position is:
$${\theta }_{\text{hour}}=(4\times 30°)+(25\times 0.5°)$$
$${\theta }_{\text{hour}}=120°+12.5°=132.5°$$

2. Calculate the position of the minute hand:
The minute hand completes a full circle of 360° in 60 minutes.
Therefore, the rate of movement of the minute hand is:
$$\frac{360°}{60\text{minutes}}=6°\text{per minute}$$ At 25 minutes, the angle moved by the minute hand from the 12 o'clock position is:
$${\theta }_{\text{minute}}=25\times 6°=150°$$

3. Calculate the absolute difference between the two angles:
The angle between the two hands is:
$$\text{Angle}=|{\theta }_{\text{minute}}-{\theta }_{\text{hour}}|$$
$$\text{Angle}=|150°-132.5°|=17.5°$$

Thus, the angle between the hour hand and the minute hand at 4:25 is 17.5°.