Final answer:
The angle between the hands of a clock at 5:30 pm is 15 degrees, with the minute hand at 180° and the hour hand at 165° from the top position.
Step-by-step explanation:
The angle between the hands of a clock can be found by calculating the angles moved by each hand from the top position of 12 o'clock. At 5:30 pm, the minute hand is at the 6, indicating that it has moved 180° from the top. The hour hand at 5:30 pm is halfway between the 5 and the 6. Since each hour represents 30° (360° divided by 12 hours), the hour hand has moved 5.5 x 30°, or 165° from the top position.
To find the angle between the two hands, we subtract the smaller angle from the larger one: 180° - 165° = 15°. Therefore, the angle between the hands of the clock at 5:30 pm is 15 degrees.
This problem is an example of a practical application of angular measurement, which is a concept covered in mathematics, particularly in the study of geometry and measurement.