Question

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

Answer 1

Answer:

20 sides

Step-by-step explanation:

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

$Each \ Interior = \frac{(n-2)*180}{n}$

Where

n is the number of sides.

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

$Each \ Interior = \frac{(n-2)*180}{n}\\162=\frac{(n-2)180}{n}\\162n=(n-2)180\\162n=180n-360\\18n=360\\n=20$

THus, the polygon has 20 sides