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In moving from one number on the clock face to the next, a hand moves $360 \div 12 ^\circ = 30 ^\circ$.
At 2.30, the hour hand will be exactly half way between the $2$ and the $3$, and the minute hand will be exactly on the $6$.
So the angle between the two hands will be $3 \times 30^\circ + 15^\circ = 105^\circ$.
Half Past Two
Age 11 to 14
ShortChallenge Level 
In moving from one number on the clock face to the next, a hand moves $360 \div 12 ^\circ = 30 ^\circ$.
At 2.30, the hour hand will be exactly half way between the $2$ and the $3$, and the minute hand will be exactly on the $6$.
So the angle between the two hands will be $3 \times 30^\circ + 15^\circ = 105^\circ$.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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