Question

If each interior angle of a regular polygon is 162 how many sides does it have

Answer 1

20 sides

Explanation:

The formula that relates interior angles with number of sides is:

`Each \ Interior = ((n-2)*180)/(n)`

Where

n is the number of sides.

We know each interior is 162 degrees, so we substitute and cross multiply and solve for n:

`Each \ Interior = ((n-2)*180)/(n)\\162=((n-2)180)/(n)\\162n=(n-2)180\\162n=180n-360\\18n=360\\n=20`

THus, the polygon has 20 sides