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

Options

A. `75^@`
B. `80^@`
C. `105^@`
D. `60^@`

Answer

A

Explanation

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


`therefore` Angle traced by the hour hand in 12 hours `=360^{circ}`


Now,


Angle traced by the hour hand in 8 hours 30 minutes, i.e., `frac{17}{2}=(frac{360}{12} times frac{17}{2})^{circ}` `=255^{circ}`


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


`therefore` Angle traced by the minute hand in 60 minutes `=360^{circ}`


Now,


Angle traced by the minute hand in 30 minutes `=(frac{360}{60} times 30^{circ})=180^{circ}`


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