The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:

Step 1: At 8:30, the minute hand is at 6 while the hour hand is halfway between 8 and 9.

Step 2: Each hour on the clock represents 30 degrees (360 degrees divided by 12 hours).

Step 3: The minute hand is 180 degrees away from the top of the clock (6 times 30).

Step 4: The hour hand is 255 degrees away from the top of the clock (8.5 times 30).

Step 5: The difference between the positions of the hour hand and the minute hand is 255 - 180 = 75 degrees.

So, the angle between the minute hand and the hour hand at 8:30 is 75 degrees.