Question

Here is a regular polygon with 9 sides

Work out the side of an exterior angle

Thanks

Answer 1

40

Explanation:

The number of sides also represents the number of angles.

Now, to find the measure of one angle we will need to find the sum of angles first and to do that, we use this very simple formula:

(n-2)*180 (n is the count of interior angles)

7*180 = 1260 and to find the measure of one angle we divide the sum with the number of angles:

1260/9 = 140

now, since the sum of an interior angle and an exterior angle is 180:

180-140 = 40 is the size of one exterior angle

There's an easier way too, just divide the sum of exterior angles by the number of angles

360/9 = 40