The angle between the minute hand and the hour hand of a clock when the time is 8:30, is:

$$\eqalign{ & {\text{Angle}}\,{\text{traced}}\,{\text{by}}\,{\text{hour}}\,{\text{hand}}\,{\text{in}}\,\frac{{17}}{2}\,{\text{hrs}} \cr & {\text{ = }}\,{\left( {\frac{{360}}{{12}} \times \frac{{17}}{2}} \right)^ \circ } \cr & = 255^ \circ \cr & {\text{Angle}}\,{\text{traced}}\,{\text{by}}\,{\text{min}}{\text{.}}\,{\text{hand}}\,{\text{in}}\,{\text{30}}\,{\text{min}} \cr & = {\left( {\frac{{360}}{{60}} \times 30} \right)^ \circ } \cr & = 180^ \circ \cr & \therefore {\text{Required}}\,{\text{angle}} \cr & = {\left( {255 - 180} \right)^ \circ } = {75^ \circ } \cr} $$