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Clock Face Angles
Age 11 to 14
ShortChallenge Level 
Each minute, the minute hand moves $\frac{360}{60} = 6^{\circ}$, so the minute hand makes an angle of $14 \times 6 = 84^{\circ}$ with the upwards vertical.
Each hour, the hour hand moves $\frac{360}{12} = 30^{\circ}$ so the hour hand makes an angle of $(8 + \frac{14}{60}) \times 30 = 247^{\circ}$ with the same vertical.
Therefore, the angle between the two hands is $247^{\circ} - 84^{\circ} = 163^{\circ}$.
Each hour, the hour hand moves $\frac{360}{12} = 30^{\circ}$ so the hour hand makes an angle of $(8 + \frac{14}{60}) \times 30 = 247^{\circ}$ with the same vertical.
Therefore, the angle between the two hands is $247^{\circ} - 84^{\circ} = 163^{\circ}$.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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