What is the exact angle formed by the hands on a clock when the time reads 9:30?

105 degrees

105 degrees: if the hour hand is right at 9, and the minute had was right at 30 then it would be 90 degrees. but since we're 30 minutes into the hr, the hour hand will be (theoretically) half waybetween 9 and 10pm. so you need to calculate that additional variation. If have the arms 3 hrs apart makes a perfect 90 degrees, then each hr would equal 30 degrees -> thus a half hr would result in a 15 degrees. 90+15= 105 degrees

Right

|0.5(60H-11M)| = 105 degrees

oops, I mean 1/4 of 360 :) 90

Dear God. There are people giving answers that aren't even close. Hopefully they're not employed in the tech industry.

You can look at it in 2 ways. First answer is the short angle which is 90+15= 105 degrees. Second answer is the long angle which is 270-15=255 degrees. The 15 degrees comes from the fact that the 9 o clock hand is not exactly on 9 anymore but between 9 and 10. from 9 to 12 = 90 degrees, so from 9 to 10 is 90/3=30 degrees, so from 9 to 9:30 = 30/2 = 15 degrees.

I'm so surprised to see so many ridiculous answers for such an easy question...

formula : |30(h)-11/2 (m)| |30(9)-5.5(30)| |270-165| 105 degrees reflex angle 360-105 225 degrees

Common response, but it's incorrect. What about the hour hand? It's not pointing directly at the 9 anymore...

60 degrees, or 300 degrees whichever way you want to look at it.

270 degrees