What will be the measurement of the angle made by the hour and minute hands of a clock when the time is 'quarter past 3'?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(7\frac{1}{2}^{\circ}\)
The minute hand moves 6° a minute (360° in 60 minutes), and the hour hand moves 0.5° a minute (30° in 60 minutes). At quarter past 3 the minute hand is on the 3, but the hour hand has moved a quarter of the way from 3 towards 4.
Hour hand: \(3\times30^{\circ}+15\times0.5^{\circ}=90^{\circ}+7.5^{\circ}=97.5^{\circ}\) from the 12
Minute hand: \(15\times6^{\circ}=90^{\circ}\) from the 12
Angle between them \(=97.5^{\circ}-90^{\circ}=7\frac{1}{2}^{\circ}\)
Tip: At H hours M minutes the angle between the hands is \(|30H-5.5M|\) degrees (take 360° minus it if it is over 180°). Here \(|30\times3-5.5\times15|=|90-82.5|=7.5^{\circ}\).