5 of 7 The interior angle of a regular polygon is 165º.
How many sides does the polygon have?

24 sides

Step-by-step explanation:

An exterior angle of a regular polygon is 360 divided by the number of sides. The exterior angle is equal to the interior angle subtracted from 180. We can say an exterior angle of this polygon is 180 - 165 or 15. From the first property, we can write an equation:

360/n = 15

360 = 15n

n = 24

24 sides

Another way to do this, is the formula for an interior angle of a regular polygon is:

180(n - 2)/n

This is equal to the interior angle:

180(n-2)/n = 165

180n - 360 = 165n

15n - 360 = 0

15n = 360

n = 24