Question

What will be the acute angle between hands of a clock at $2:30$?

• A. ${105}^o$
• B. ${115}^o$
• C. ${95}^o$
• D. ${135}^o$

Answer 1

The correct option is A ${105}^o$

Every number in the watch have ${30}^0$ step

So when clock shows $2:30$ it implies that minute hand is at $6$ and hour hand is in exactly middle of $2$ and $3$

Therefore,The angle between minute hand and $3$ is ${15}^o$

Total angle between minute hand and hour hand is

angle between $3$ and $6$ +angle between min. hand and $3$

$={30}^0+{30}^0+{30}^0+{15}^0={105}^0$

Hence, option A.