Question

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

• A. ${80}^{\circ }$
• B. ${75}^{\circ }$
• C. ${60}^{\circ }$
• D. ${105}^{\circ }$

Answer 1

The correct option is B

${75}^{\circ }$

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 $=(\frac{360}{60}\times {30}^{\circ })={180}^{\circ }$

$\therefore$ Required angle between two hands of the clock = ${255}^{\circ }-{180}^{\circ }={75}^{\circ }$