Final answer:
To find the angle between the hour and minute hands of a clock, consider the positions of the hands in terms of the hour and the minute. At 11:20, the angle between the hands is 306 degrees. At 5:45, the angle between the hands is 120 degrees. At 2:25, the angle between the hands is 90 degrees.
Step-by-step explanation:
To find the angle between the hour and minute hands of a clock, we need to consider the positions of the hands in terms of the hour and the minute. The hour hand moves 360 degrees in 12 hours, or 30 degrees per hour. The minute hand moves 360 degrees in 60 minutes, or 6 degrees per minute.
i) At 11:20, the hour hand is at the 11th hour, which is 330 degrees (11 * 30). The minute hand is pointing at the 4th minute, which is 24 degrees (20 * 6). The angle between the hands is the difference between these two angles, which is 306 degrees.
ii) At 5:45, the hour hand is at the 5th hour, which is 150 degrees (5 * 30). The minute hand is pointing at the 45th minute, which is 270 degrees (45 * 6). The angle between the hands is the difference between these two angles, which is 120 degrees.
iii) At 2:25, the hour hand is at the 2nd hour, which is 60 degrees (2 * 30). The minute hand is pointing at the 25th minute, which is 150 degrees (25 * 6). The angle between the hands is the difference between these two angles, which is 90 degrees.