# Handy Angles

Weekly Problem 39 - 2008

How big is the angle between the hour hand and the minute hand of a clock at twenty to five?

How big is the angle between the hour hand and the minute hand of a clock at twenty to five?

## Problem

How big is the angle between the hour hand and the minute hand of a clock at twenty to five?

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

## Student Solutions

Let $x$ denote the angle between the hour hand and the vertical, and $y$ the angle between the minute hand and the vertical.

Image

$\frac{360}{12}=30$ so we calculate that $x = \left( 4+\frac{2}{3} \right) \times 30 =140^\circ$ and $y = 8 \times 30 = 240^\circ$.

The angle between the hands is $y - x = 240^\circ - 140^\circ = 100^\circ$.