What is the larger angle between the hands of a clock at 6:40 a.m.?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 320°
The two hands make two angles that together form a full turn of 360°. Find the smaller one first, with the minute hand at 6° a minute and the hour hand at 30° an hour plus 0.5° a minute, then subtract it from 360°.
Hour hand at 6:40: \(6\times30^\circ+40\times0.5^\circ=180^\circ+20^\circ=200^\circ\)
Minute hand at 40 minutes: \(40\times6^\circ=240^\circ\)
Smaller angle \(=240^\circ-200^\circ=40^\circ\)
Larger angle \(=360^\circ-40^\circ=320^\circ\)
