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

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
$$\eqalign{ & \Rightarrow x = {\left( {30 \times 8\frac{1}{2}} \right)^ \circ } \cr & \Rightarrow x = {\left( {30 \times \frac{{17}}{2}} \right)^ \circ } \cr & \Rightarrow x = {255^ \circ } \cr} $$
The minute hand make the angle in 1 minute = 6°
Minute hand makes the angle in 30 minutes
$$\eqalign{ & {\text{ = }}{\left( {6 \times 30} \right)^ \circ } \cr & = {180^ \circ } \cr & {\text{Required angle}} \cr & = {255^0} - {180^0} \cr & = {75^0} \cr} $$