What will be the measurement of the angle made by the hands of a clock when the time is 6:14?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 103°
The minute hand turns \(360^\circ\) in 60 minutes, that is \(6^\circ\) per minute. The hour hand turns \(30^\circ\) in an hour, that is \(0.5^\circ\) per minute. Both are measured from the 12.
Hour hand at 6:14: \(6\times30^\circ+14\times0.5^\circ=180^\circ+7^\circ=187^\circ\)
Minute hand at 14 minutes: \(14\times6^\circ=84^\circ\)
Angle between them \(=187^\circ-84^\circ=103^\circ\)
Shortcut: At H hours M minutes, the angle is \(\left|30H-\frac{11}{2}M\right|\): \(\left|180-77\right|=103^\circ\).