Final answer:
The angle measure between the hands of an analog clock at 2:22 is 112 degrees.
Step-by-step explanation:
To find the angle measure between the hands of an analog clock at 2:22, we need to determine the positions of the hour and minute hands. At 2:22, the hour hand will be slightly past 2, pointing towards the number 3. Since the hour hand moves 1/12th of a revolution per hour, we can calculate the angle it has moved from the starting position at 2 o'clock. The minute hand will be pointing towards the number 4, which is 2/3 of the way between 2 and 3. The minute hand moves 1/60th of a revolution per minute.
Now, we can calculate the angles. Starting with the hour hand, it has moved 2/3 of the way from 2 to 3, which is (2/3) * (1/12) * 360 degrees = 20 degrees. The minute hand has moved 22 minutes * (1/60) * 360 degrees = 132 degrees. To find the angle between the hands, we subtract the angle of the hour hand from the angle of the minute hand: 132 degrees - 20 degrees = 112 degrees.
Therefore, the angle measure between the hands of an analog clock at 2:22 is 112 degrees.