At 8 : 30, the hour hand and the minute hand of clock form an angle of = ?

Answer: Option B

In 1 hour, the hour hand make the angle of 30°
The hour hand make the angle of x in $$\text{8}\frac{30}{60}$$ hours
$$\begin{array}{rl}& \Rightarrow x={\left(30\times 8\frac{1}{2}\right)}^{\circ }\\ & \Rightarrow x={\left(30\times \frac{17}{2}\right)}^{\circ }\\ & \Rightarrow x=255^{\circ }\end{array}$$
The minute hand make the angle in 1 minute = 6°
Minute hand makes the angle in 30 minutes
$$\begin{array}{rl}& \text{ = }{\left(6\times 30\right)}^{\circ }\\ & =180^{\circ }\\ & \text{Required angle}\\ & =255^0-180^0\\ & =75^0\end{array}$$