If it is 9:15, what is the angle between the hour and minute hands?

If it is 9:15, what is the angle between the hour and minute hands?

Step 1: Understand that the clock is divided into 12 hours, and each hour represents 30 degrees (360 degrees / 12 hours = 30 degrees per hour).
Step 2: Calculate the position of the hour hand. At 9:00, the hour hand is at 9 * 30 = 270 degrees. Since it is now 9:15, the hour hand has moved a little further.
Step 3: The hour hand moves 0.5 degrees for each minute (30 degrees per hour / 60 minutes = 0.5 degrees per minute). So, in 15 minutes, it moves 15 * 0.5 = 7.5 degrees.
Step 4: Add the movement of the hour hand to its position at 9:00. So, 270 degrees + 7.5 degrees = 277.5 degrees.
Step 5: Calculate the position of the minute hand. At 15 minutes, the minute hand is at 15 * 6 = 90 degrees (since each minute represents 6 degrees).
Step 6: Find the angle between the hour and minute hands by taking the absolute difference: |277.5 - 90| = 187.5 degrees.
Step 7: Since angles on a clock can be measured in two ways (the smaller angle and the larger angle), we need to find the smaller angle. The smaller angle is 360 degrees - 187.5 degrees = 172.5 degrees.

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