What is the angle formed by the hands of the clock when it is 1:45?

142.5 degrees. If we just think of the clock hour hand at 1 and the minute hand at the 45 position (near 9 o’clock), that is 120 degrees since they are 4 “numbers” apart, and each number on the clock represents 30 degrees (360/12).

However, recall that the hour hand has already moved by the time the minute hand has reached the 45 position – it is now closer to 2 o’clock. 45 represent ¾ of an hour, so the hour hand will have moved ¾ of 30 degrees, or 22.5 degrees. If we add them together, we see that 120 + 22.5 = 142.5

The most common mistake is to state the original number we arrived at – 120 degrees – rather than finishing the calculation. Sometimes with this type of question the interviewer will lead you in the right direction if you have a basic idea of how to solve it.