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??

Answer 1

triangle has 180° total
square has 360° total
pentagon has 540° total
hexagon has 720° total
so they increase by 180° for every side to the polygon starting at 3 sides instead of 1 so if n is how many sides in the polygon then
(n-2)×180=degrees TOTAL inside the polygon
(n-2)×180/n=degrees for EACH angle in the polygon

(n-2)×180/n=162
multiply both sides by n
(n-2)×180=162n
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
Icosagon is the term for a 20 sided polygon

Answer 2

Gear have 20 sides .

Explanation:

Given : A company is manufacturing a gear in the shape of a regular polygon. The measure of each angle of the gear is 162º.

To find : How many sides does the gear have.

Solution : We have given that each angle of polygon = 162 degree.

By the property of polygon :

Each angle of polygon =
`((n-2)180)/(n)`.

Where, n is number of sides polygon .

Plugging the values,

162 ° =
`((n-2)180)/(n)`.

On simplify right side , we can write it as:

162 ° =
`(180n)/(n) -(360)/(n)`.

162 ° = 180 -
`(360)/(n)`.

On subtracting by 180 both side.

162 -180 = -
`(360)/(n)`.

-18° = -
`(360)/(n)`.

On multiplying by n both side

-18° × n = -360°

On dividing by - 18 by both side

n =
`(360)/(18)`.

n = 20 .

Therefore , gear have 20 sides .