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

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

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

Now,Angle traced by the hour hand in 8 hours 30 minutes, i.e., 172 = 36012×172°=255°">Now,