Claudia, this might be best answered graphically, by drawing an example, but try to picture this: If the 12 on the clock were at 0-degrees, and the 3 were at 90 degrees, then the six would be at 180 degrees, right? Because a complete circle has 360 degrees. The big hand would be pointing straight down toward the six, or 180-degrees around the clock circle. The 8, is 8/12's of the way around the circle, and 360/12 is 30, so each number on the clock is 30 degrees around the circle. The 8 is therefore (8*30) 240 degrees around the circle. So if the hour hand was on the 8, and the minute hand was on the 6, the hands of the clock are 60 degrees apart...the minute hand is pointing at the number 6, or 180 degrees, and the hour hand is pointing toward the number 8, or 240 degrees around the circle. A 60-degree difference. All this would be true, except when it is 8:30, the hour hand does not actually point directly at the number 8. It points half way between the 8 and the 9 - an additional 15-degrees of hand rotation. So, the real answer is 75 degrees..the real life, actual mechanical clock difference in hand position ona 12 hour clock. Hope this helps!
I should add....that's the easy way to do it for a 12-hour clock. The acute angle is 75, the obtuse angle is 285 degrees. There is a lengthy trig function for it, but I think youre looking for a more simple answer.
