Question

Find the smaller angle made between the hour and the minute hands of a clock when the time is 9:00 PM.

• A. ${80}^{\circ }$
• B. ${75}^{\circ }$
• C. ${90}^{\circ }$
• D. ${85}^{\circ }$

Answer 1

The correct option is C

${90}^{\circ }$

The angle between any two consecutive numbers on the clock is $\frac{360}{12}={30}^{\circ }.$

There are 3 such angles when the clock reads 09:00 PM as illustrated below.


$\therefore$ The angle made by the hands of the clock is $3\times {30}^{\circ }={90}^{\circ }.$