Question

A company is manufacturing a gear in the shape of a regular polygon. The measure of each angle of the gear is 162º. How many sides does the gear have? 19 18 20 21

Answer 1

Let us have a recap first.

For triangle it's 180 degrees in total
Square has 360 degrees in total
Pentagon has 540 degrees total
Hexagon has 720 degrees in total

So these polygons increase by 180 degrees for every side to the polygon starting at three sides instead of one.
Let:

n = number of sides in the polygon

(n-2) * 180 = degrees total inside the polygon
(n-2) * 180 / n = degrees for each angle in polygon

Substitute:

(n-2) * 180 / n = 162
multiply both sides by n
(n-2) * 180 = 162n
then divide both sides by 180

n-2 = 162n / 180
n-2 = 0.9n
subtract 0.9n and add 2 to both sides to get n alone
0.1n = 2

n = 20 sides
Thus,

Icosagon (20-gon) is the term for a 20 sided polygon