How many minutes have passed if the minute hand has moved to 162 degrees

For the minute hand, this is 27 minutes from the on-the-hour angle of zero degrees, so the angle is (27 minutes) * ((360 degrees) / (60 minutes)) = 162 degrees. [Note: 30 minutes is 180 degrees, so this makes sense.] (27 minutes) * ((360 degrees) / (12 hours)) * ((1 hour) / (60 minutes)) = 13.5 degrees