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Well, the minute hand traverses 360 degrees in 1 hour.Or 360 degrees/60 minutes = 6 degrees per minute.So 12 minutes = 6 x 12=72 degrees in 12 minutes.[Remember 15 minutes = 90 degrees.]
It is 82 degrees and 12 minutes, as in the question = 82.2 deg = 1.4347 radians.
60 minutes = 1 rotation = 360 degrees So 12 minutes = 360*12/60 = 72 degrees.
60 degree angle at 4:12 At 4.00 the angle is 120 degrees. In 12 minutes the minute hand moves 72 degrees while the hour hand moves 6 degrees. So that 120 degree angle reduces by 66 degrees in 12 minutes, and the answer is 54 degrees.
72 degrees 12/60 of 360 = 1/5 x 360 = 72