What is the angle between the hands when it is quarter past 3

7.5 degrees

7.5 degrees. The hour hand would have moved past 3 in order for it to be 3:15.

Time for me to go

Depends on the clock. For starters let's assume it's an analogue display. If the hour hand only moves on the hour as opposed to at a set rate around the clock, then it would be 0. If it moves at a set rate, then the angle would be 7.5 degrees. (Full circle is 360 degrees, 12 hours on the face so it moves 30 degrees every hour or 7.5 degrees every quarter hour).

360 degree

3.5 degrees

Near enough to 0 to not worry about, I am sure there is a website with a more accurate answer if you really want to know. This is interesting as the question is/was "If the time is quarter past 3, what is the angle measurement on the clock?" What are we measuring? If everything was plumb and level then it might 90 degrees. I know the table my digital clock sits on is not level but I have never measured the wonkyness of the table.

7.5 degrees.

I really don't care

Gillian, Please put on this nice pointy hat and sit in the corner.... Quarter past 3 = 180 degrees? Are you sure about that?

90 degrees acutely and 270 degrees obtusely

No scrub that the answer I gave was for 3 o'clock. 3.15 would be 7.5 degrees or inversely 352.5 degrees.

It's on the right hand side about a quarter of the way round the clock.

7.5 degrees

The minutes hand stood at 90 deg the 15 minutes lapse will move the hour hand to 90 + (15/60 * 30 deg) = 97.5 deg difference = 7.5 deg

Somewhere between minus and plus infinity. Modulus 360 degrees, of course.

7.5 degrees. The minute hand will be 90 degrees past the vertical, the hour hand (which moves 30 degrees per hour) has moved 3.25 * 30 degrees since noon so is at 97.5 degrees past vertical. Difference = 7.5 degrees.

1. Discreet-placed arrows clock. 0 degrees 2. Ordinary clock 360/12/(1/4) = 7.5 degrees

I'm Sorry. 360/12*(1/4) = 7.5

Well each hour mark on the clock is 30 degrees from 12pm. The hour hand moves 30 degrees per 1 hour, 15 degrees per half hour, 7.5 degrees per 15minutes. The minute hand is at 90 degrees from 12pm and the hour hand is at 97.5 degrees from 12pm. The difference is then, as many others have said, 7.5 degrees.

180 degrees

180 degrees