The time in a clock is 20 minute past 2. What is the angle between the minute and hour hands of the clock?

Step 1: Understand the position of the clock hands. At 20 minutes past 2, the minute hand is on the number 4, and the hour hand is somewhere between the numbers 2 and 3.

Step 2: Calculate the position of the hour hand. The hour hand moves 0.5 degrees per minute (360 degrees / 12 hours / 60 minutes = 0.5 degrees per minute). Since it's 20 minutes past 2, the hour hand has moved 10 degrees past the number 2 (20 minutes * 0.5 degrees per minute = 10 degrees).

Step 3: Calculate the position of the minute hand. The minute hand moves 6 degrees per minute (360 degrees / 60 minutes = 6 degrees per minute). Since it's 20 minutes past the hour, the minute hand is 120 degrees from the top of the clock (20 minutes * 6 degrees per minute = 120 degrees).

Step 4: Calculate the angle between the hour and minute hands. The hour hand is 60 degrees from the top of the clock (2 hours * 30 degrees per hour = 60 degrees) plus the extra 10 degrees it has moved, for a total of 70 degrees. The minute hand is 120 degrees from the top of the clock. So, the angle between the hour and minute hands is 120 degrees - 70 degrees = 50 degrees.