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.