Question

Find the angle between the minute hand and the hour hand of a clock when the time is 7:20 AM in degrees

Answer 1

We know that the hour hand completes one rotation in 12h, while the minute hand completes one rotation in 60 min.
Therefore, the angle traced by the hour hand in 12h is ${360}^{\circ }$.
Angle traced by the hour hand in 7 h 20 min, i.e., $\frac{22}{3}h={(\frac{360}{12}\times \frac{22}{3})}^{\circ }={220}^{\circ }$
Also, Angle traced by the minute hand in 60 min$={360}^{\circ }$
Angle traced by the minute hand in 20 min$={(\frac{360}{60}\times 20)}^{\circ }={120}^{\circ }$
Hence, Required angle between the two hands$={220}^{\circ }-{120}^{\circ }={100}^{\circ }$
Ans: 100