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Question

The angle between the minute and hour hands of a clock at 8:30 is


  1. 105

  2. 80

  3. 75

  4. 60


Solution

The correct option is C

75


We know that the hour hand of a clock completes one rotation in 12 hours.

Angle traced by the hour hand in 12 hours =360

Now,

Angle traced by the hour hand in 8 hours 30 minutes, i.e., 172=(36012×172) 

=255

We also know that the minute hand of a clock completes one rotation in 60 minutes.

Angle traced by the minute hand in 60 minutes =360

Now,

Angle traced by the minute hand in 30 minutes =(36060×30)=180

Required angle between two hands of the clock = 255180=75

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