Final answer:
To find the angle measure between the clock hands at 5:18 PM, calculate the position of each hand and subtract the lesser angle from the greater one. The minute hand's position is 108 degrees, and the hour hand's position is at 159 degrees from the top of the clock. The correct small angle between them is 51 degrees, which doesn't match any of the provided options.
Step-by-step explanation:
To determine the angle measure between the hour hand and minute hand of a clock at 5:18 PM, we can use the following method:
- The minute hand is at 18 minutes, which is 18/60 = 3/10 of the way around the clock. Since there are 360 degrees in a full circle, the minute hand is 360 degrees * 3/10 = 108 degrees from the top of the clock.
- The hour hand is at 5 hours plus 18 minutes past the hour, which means it has moved 5 hours * 30 degrees/hour = 150 degrees plus 18/60 * 30 degrees = 9 degrees for the additional minutes. So, it has moved a total of 150 degrees + 9 degrees = 159 degrees from the top of the clock.
- To find the angle between the hands, we subtract the lesser angle from the greater angle. We can take either 159 degrees - 108 degrees = 51 degrees or we can use the complementary angle which is 360 degrees - 159 degrees + 108 degrees = 309 degrees. So the smaller angle between the clock hands is 51 degrees.
However, none of the available options A (90 degrees), B (100 degrees), C (108 degrees), or D (120 degrees) match the calculated angle of 51 degrees. The most likely explanation is that there is a mistake in the question or the provided options.