Question

Find the angle between the two hands of a clock of $15$ minutes past $4$ O' clock.

• A. ${38.5}^{\circ }$
• B. ${36.5}^{\circ }$
• C. ${37.5}^{\circ }$
• D. None of these

Answer 1

Answer: (C)

${37.5}^{\circ }$

Angle traced minutes hand in $15$ minutes $=\frac{15\times 360}{60}={90}^{\circ }$
The hour hand traces half a degree in one minute.

Hence, angle traced by hour hand at $4$ hour and $15$ minutes $=4\times {30}^o+\frac{{15}^o}{2}={127.5}^{\circ }$
Thus, angle between two hands $=127.5-90={37.5}^{\circ }$