Question

Jenny is looking at a clock striking 4:25. What will the reflection angle formed between the hands of the clock be?

Answer 1

Given:

The time is 4:25.

We know that the angle covered by the minute hand in 1 hour = 360°

∴ Angle made by the minute hand in 25 $\text{minutes}=\frac{25\times 360}{60}=150°$

We know that the angle covered by the hour hand in 12 hours = 360°

$\text{So, the hour hand traces}=\frac{360°}{12\times 60}$
$=\frac{1}{2}°\text{half a degree in one minute.}$

Hence, angle traced by the hour hand at 4 hours and 25 minutes
$=\text{Number of hours}\times 30°$

$+\text{Number of minutes}\times \frac{1}{2}°$


$=\text{Number of hours}\times 30°$

$+\frac{\text{Number of minutes}}{2}$

$=4\times 30°+\frac{25}{2}=120°+12.5°=132.5°$

Thus, angle formed at 4:25 between 2 $\text{hands is}=150°–132.5°={17.5}^{\circ }$

Hence, the reflection angle formed
$=360°–17.5°={342.5}^{\circ }$