Question

The angle between the minute hand and the hour hand of a clock when the time is $7:20\text{a.m.}$ is

Answer 1

Let's draw the clock

$7\text{hr}20min=7+\frac{20}{60}=\frac{22}{3}\text{hr}$
We know that hour hand complete 1 rotation in $12$ hr, while the minute hand complete 1 rotation in $60$ min.

Angle traced by hour hand in $12$ hr is ${360}^{\circ }$
$7\text{hr}20min={(\frac{22}{3}\times \frac{360}{12})}^{\circ }={220}^{\circ }$

Angle traced by minute hand in $60$ min is ${360}^{\circ }$ in $20min={(\frac{360}{60}\times 20)}^{\circ }={120}^{\circ }$

Hence, required angle between the two hands $={220}^{\circ }-{120}^{\circ }={100}^{\circ }$