Find the smaller angle formed by the hands of a clock when it shows 7:20 in the morning.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 100°
Measure both hands clockwise from 12: the minute hand at 6° a minute, the hour hand at 30° an hour plus 0.5° a minute.
Hour hand at 7:20: \(7\times30^\circ+20\times0.5^\circ=210^\circ+10^\circ=220^\circ\)
Minute hand at 20 minutes: \(20\times6^\circ=120^\circ\)
Difference \(=220^\circ-120^\circ=100^\circ\), which is less than 180°, so it is the smaller angle
260° \((=360^\circ-100^\circ)\) is the larger angle, and 90° leaves out the 10° the hour hand moves past the 7 in 20 minutes
