What will be the angle between hour hand and minute hand of the clock at 7:15?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 127.5°
The minute hand turns 6° a minute, and the hour hand turns 0.5° a minute (30° an hour), so at 7:15 the hour hand has moved a quarter of the way from 7 to 8. Both positions are measured clockwise from 12.
Minute hand: \(15\times6^\circ=90^\circ\) (at 3)
Hour hand: \(7\times30^\circ+15\times0.5^\circ=210^\circ+7.5^\circ=217.5^\circ\)
Angle between them \(=217.5^\circ-90^\circ=127.5^\circ\)
Shortcut: The angle at H hours M minutes is \(\left|30H-\frac{11}{2}M\right|\).
\(\left|30\times7-\frac{11}{2}\times15\right|=|210-82.5|=127.5^\circ\)