PREVIOUSLY ASKED IN:
WBPSC Miscellaneous Preliminary 2023
Answer
\( 180^\circ \)
Explanation
The exact angle between clock hands is found using \( |30H - 5.5M| \). For 9:15, \( H=9 \) and \( M=15 \). Calculation: \( |270 - 82.5| = 187.5^\circ \). The reflex angle is \( 187.5^\circ \), making the interior angle \( 360 - 187.5 = 172.5^\circ \). Since 172.5 is not in the options, the question assumes a static hour hand. If the hour hand stays exactly at 9 and the minute hand is exactly at 3, they are strictly opposite, forming a \( 180^\circ \) straight line.
Key Points
- > Formula for angle: \( \theta = |30H - 5.5M| \).
- > Mathematically exact answer: \( 172.5^\circ \).
- > Positions 9 and 3 are diametrically opposite on the clock face.
- > The minute hand moves \( 6^\circ \) per minute.
- > The hour hand moves \( 0.5^\circ \) per minute.
- > In 15 minutes, the hour hand moves \( 7.5^\circ \) away from 9.
- > The examiner provided 180 by ignoring the hour hand's micro-movement.
Additional Information
Clock Hand Mechanics
| Hand | Movement per Hour | Movement per Minute |
|---|---|---|
| Hour Hand | \( 30^\circ \) | \( 0.5^\circ \) |
| Minute Hand | \( 360^\circ \) | \( 6^\circ \) |
| Second Hand | \( 21600^\circ \) | \( 360^\circ \) |
Memory Tips
- Straight Line: At exactly 9:15, visually, the hands are at 9 and 3, which looks like a straight horizontal line (\( 180^\circ \)), even though in reality the hour hand has moved slightly up.