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:
Gear have 20 sides .
Step-by-step 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 = [tex]\frac{(n-2)180}{n}[/tex].
Where, n is number of sides polygon .
Plugging the values,
162 ° = [tex]\frac{(n-2)180}{n}[/tex].
On simplify right side , we can write it as:
162 ° = [tex]\frac{180n}{n} -\frac{360}{n}[/tex].
162 ° = 180 -[tex]\frac{360}{n}[/tex].
On subtracting by 180 both side.
162 -180 = -[tex]\frac{360}{n}[/tex].
-18° = - [tex]\frac{360}{n}[/tex].
On multiplying by n both side
-18° × n = -360°
On dividing by - 18 by both side
n = [tex]\frac{360}{18}[/tex].
n = 20 .
Therefore , gear have 20 sides .
