Question

a circular dial has nine equally spaced points, as shown. point a is on the top of the dial. suppose that the dial is turned clockwise until point e is on top. how many degrees does the dial have to turn?

Explanation:

Step1: Find angle between adjacent points

The total angle around a circle is $360^{\circ}$. There are 9 equally - spaced points. So the angle between adjacent points is $\frac{360^{\circ}}{9}=40^{\circ}$.

Step2: Count number of intervals

To get from point A to point E clock - wise, we count the number of intervals between them. There are 4 intervals.

Step3: Calculate total angle turned

The total angle the dial has to turn is the number of intervals times the angle between adjacent points. So the angle is $4\times40^{\circ}=160^{\circ}$.

Answer:

$160$