Question

What is the angle between the minute hand and the hour hand of a clock when the time is 4:20

Answer 1

4 hours and 30 minutes can be written as $\frac{13}{3}$ hours.
Angle traced by hour hand in $\frac{13}{3}$ hours = $\frac{360}{12}\times \frac{13}{3}$ =${130}^{\circ }$
Angle traced by min. hand in 20 min. = $\left(\frac{360\times 20}{60}\right){}^{\circ }$
Required angle = $(130-120{)}^{\circ }={10}^{\circ }$.