Final answer:
The angle between the hour hand and the minute hand of a clock showing 9:00 a.m. is 270 degrees.
Step-by-step explanation:
In order to find the angle between the hour hand and the minute hand of a clock showing 9:00 a.m., we need to determine the positions of both hands at that time. At 9:00 a.m., the hour hand points directly at the 9 and the minute hand points directly at the 12. To find the angle between the two hands, we need to calculate the angle formed by the hour hand with the 12 o'clock position and subtract the angle formed by the minute hand with the 12 o'clock position.
The hour hand moves 360 degrees in 12 hours, so in 1 hour, it moves 360/12 = 30 degrees. At 9:00 a.m., the hour hand has moved 9 hours, so it is at the 9 o'clock position, which is 9 * 30 = 270 degrees from the 12 o'clock position. The minute hand moves 360 degrees in 60 minutes, so in 1 minute, it moves 360/60 = 6 degrees. At 9:00 a.m., the minute hand has not moved, so it is 0 degrees from the 12 o'clock position.
Now we can find the angle between the two hands by subtracting the angle of the minute hand from the angle of the hour hand: 270 degrees - 0 degrees = 270 degrees.