Question

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

Options

• 80°

• 75°

• 60°

• 105°

Answer 1

 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 . , \[\frac{17}{2} = \left( \frac{360}{12} \times \frac{17}{2} \right)^\circ= 255^\circ\]
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 = \[\left( \frac{360}{60} \times 30 \right)^\circ= 180^\circ\]
∴ Required angle between the two hands of the clock =

\[255^\circ - 180^\circ = 75^\circ\]