To determine the angle through which the minute hand of a clock turns in 45 minutes, follow these steps:
1. Understand the movement of the minute hand:
- The minute hand completes one full rotation (360 degrees) in 60 minutes.
2. Determine the degrees per minute:
- Since the minute hand covers 360 degrees in 60 minutes, we can calculate the degrees turned per minute:
[tex]\[
\text{Degrees per minute} = \frac{360 \text{ degrees}}{60 \text{ minutes}} = 6 \text{ degrees per minute}
\][/tex]
3. Calculate the angle turned in 45 minutes:
- Now, multiply the number of degrees per minute by the number of minutes:
[tex]\[
\text{Angle turned in 45 minutes} = 6 \text{ degrees per minute} \times 45 \text{ minutes} = 270 \text{ degrees}
\][/tex]
Thus, the minute hand of the clock turns through an angle of 270 degrees in 45 minutes. The correct answer is [tex]\( 270^\circ \)[/tex].
