The angle between the minute and hour hands of a clock at 8:30 is 1) 80 ∘ 2) 75 ∘ 3) 60 ∘ 4) 105 ∘

Question

The angle between the minute and hour hands of a clock at 8:30 is 1)       80          ∘      2)       75          ∘      3)       60          ∘      4)       105          ∘

Diamond Stephens · Accepted Answer

We know that the hour hand of a clock rotates once every 12 hours.Therefore, angle traced by the hour hand in 12 hours =      75          ∘      Next,Angle traced by the hour hand in 8 hours 30 minutes, i.e.,       17    2    =  (      360    12    ×      17    2    )  =      255          ∘      We also know that a clock&#039;s minute hand completes one rotation in 60 minutes.Therefore, angle traced by the minute hand in 60 minutes   =      360          ∘      Now,Angle traced by the minute hand in 30 minutes   =  (      360    60    ×      30          ∘        )  =      180          ∘      Therefore, required angle between two hands of the clock   =      255          ∘        −      180          ∘        =      75          ∘      Answer:       75          ∘

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

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