Question

Observe that, at any instant, the minute and hour hands of a clock make two angles between them whose sum is ${360}^o$. At $6:15$ what is the difference between these two angles is$?$

• A. ${165}^o$
• B. ${170}^o$
• C. ${175}^o$
• D. ${180}^o$

Answer 1

The correct option is A ${165}^o$

At $6:15$, the smaller angle between hour hand and minute hand is $30+30+30+7.5={97.5}^o$ ...(Since the angle between $3$ and $4,4$ and $5,5$ and $6$ is ${30}^o$ each and hour hand moves ${7.5}^o$ in fifteen minutes)

$\Rightarrow$ The bigger angle would be $360-97.5={262.5}^o$

The difference between these two angles is therefore $262.5-97.5={165}^o$