The Watch Puzzle

The Angles of Time

Ian Christie, of West Virginia University, posed the following question:

Consider the angle between the hour and minute hands of a clock; Starting at noon, watch the clock very carefully, and tell me the exact time when:

1. the hands are perfectly lined up again (on top of each other);
2. the hands are pointing in exactly opposite directions;
3. the hands form an exact angle of 90 degrees;

A Couple Minutes

Will Shortz, on the NPR show "Weekend Edition", asked the question:

"The long (minute) hand of a very accurate timepiece is pointing exactly at a full minute, while the short (hour) hand is pointing to a mark exactly two minutes away. What time is it?"

I give up, show me the solution.