Question

The angle between the minute and hour hands of a clock at 8:30 is
(a) 80°
(b) 75°
(c) 60°
(d) 105°

Answer 1

(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°
$$\begin{gathered} \mathrm{Now}, \\ \mathrm{Angle}\mathrm{traced}\mathrm{by}\mathrm{the}\mathrm{hour}\mathrm{hand}\mathrm{in}8\mathrm{hours}30\mathrm{minutes},\mathrm{i}.\mathrm{e}.,\frac{17}{2}={\left(\frac{360}{12}\times \frac{17}{2}\right)}^{°}=255° \end{gathered}$$
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°
$$\begin{gathered} \mathrm{Now}, \\ \mathrm{Angle}\mathrm{traced}\mathrm{by}\mathrm{the}\mathrm{minute}\mathrm{hand}\mathrm{in}30\mathrm{minutes}={\left(\frac{360}{60}\times 30\right)}^{°}=180° \end{gathered}$$
∴ Required angle between the two hands of the clock = $255°-180°=75°$