# Half Past Two

Weekly Problem 21 - 2009

What is the angle between the two hands of a clock at 2.30?

What is the angle between the two hands of a clock at 2.30?

## Problem

What is the angle between the two hands of a clock at 2.30?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

## Student Solutions

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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 $3 \times 30^\circ + 15^\circ = 105^\circ$.