Question

From 3 o'clock to 3:45 how many degrees is that

Answer 1

It's a period of time equal to 45 minutes.
___________________________

Since I posted this answer, crowds of people have complained
that I should have said how many degrees, not how many minutes. 

The problem is:  '3 o,clock' and '3:45' are not angles.  They're both times. 
I knew that right away, as soon as you called the first one ' o'clock '.  So
right there, I knew that we weren't dealing with angles.  The only way
I knew to answer the question was in terms of time.

Answer 2

Every 15 minutes is 7.5 degrees times by 3 is 22.5 degrees to get to 3:45