From the given options, at what angle are the hands of a clock inclined at 10 minutes to 2 (Smaller angle)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 115°
10 minutes to 2 is 1:50. Each hand is measured clockwise from the 12: the minute hand moves \(6^\circ\) a minute, and the hour hand moves \(30^\circ\) an hour and also \(0.5^\circ\) a minute, so at 1:50 it is short of the 2.
Minute hand at 50 minutes: \(50\times6^\circ=300^\circ\)
Hour hand at 1 hour 50 minutes: \(30^\circ\times1+0.5^\circ\times50=30^\circ+25^\circ=55^\circ\)
Angle between them: \(300^\circ-55^\circ=245^\circ\)
The smaller angle is the other way round: \(360^\circ-245^\circ=115^\circ\)
Tip: At H hours M minutes, the angle between the hands is \(\left|30H-5.5M\right|\) degrees; here \(\left|30-275\right|=245^\circ\). When the result is more than \(180^\circ\), take \(360^\circ\) minus it for the smaller angle.