| The angle between the minute hand and the hour hand of a clock when the time is 8 : 30, is |
A) \[80{}^\circ \]
B) \[60{}^\circ \]
C) \[75{}^\circ \]
D) \[105{}^\circ \]
Correct Answer: C
Solution :
| Angle traced by hour hand in\[12\,h=360{}^\circ \] |
| Angle traced by hour hand in \[8\frac{1}{2}=\left( \frac{17}{2} \right)h\] |
| \[=\frac{360{}^\circ }{12}\times \frac{17}{2}=15\times 17=255{}^\circ \] |
| Angle traced by minute hand in 60 min \[=360{}^\circ \] |
| Angle traced by minute hand in 1 min \[=6{}^\circ \] |
| Angle traced by minute hand in 30 min \[=180{}^\circ \] |
| \[\therefore \]Required angle \[=(-180{}^\circ +255{}^\circ )=75{}^\circ \] |
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