Polygons
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Geometry
Polygons
 
 
Find / Calculate / Determine
The Number Of Sides Of A Regular Polygon When We Know The Exterior Angle
 
Find The Number Of Sides
Of A Regular Polygon With Exterior Angle Of 40°

Number of sides of a regular polygon = 360/(exterior angle)
Exterior angle = (40)
Number of sides = 360/(40) = 9

 
 

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How can we calculate
the number of sides
of a regular polygon?

Divide 360°
by the exterior angle
of the regular polygon

Why does this work?
If you walk around any polygon
you will turn at each corner
and you will end up facing
the same way as when you started
.... thus you have turned 360 degrees
.... with equal degrees at each corner

How can we calculate
the number of sides
of a regular polygon?

360° ÷ (exterior angle)
360/(exterior angle)

Calculating The Number Of Sides
Of A Regular Polygon
Using The Formula
Number Of Sides = 360/(exterior angle)

Calculate the number of sides of a regular polygon with exterior angle of 120°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (120)
Number of sides of regular polygon
= 360/(120) = 3

Calculate the number of sides of a regular polygon with exterior angle of 90°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (90)
Number of sides of regular polygon
= 360/(90) = 4

Calculate the number of sides of a regular polygon with exterior angle of 72°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (72)
Number of sides of regular polygon
= 360/(72) = 5

Calculate the number of sides of a regular polygon with exterior angle of 60°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (60)
Number of sides of regular polygon
= 360/(60) = 6

Calculate the number of sides of a regular polygon with exterior angle of 45°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (45)
Number of sides of regular polygon
= 360/(45) = 8

Calculate the number of sides of a regular polygon with exterior angle of 40°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (40)
Number of sides of regular polygon
= 360/(40) = 9

Calculate the number of sides of a regular polygon with exterior angle of 36°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (36)
Number of sides of regular polygon
= 360/(36) = 10

Calculate the number of sides of a regular polygon with exterior angle of 30°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (30)
Number of sides of regular polygon
= 360/(30) = 12

Calculate the number of sides of a regular polygon with exterior angle of 20°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (20)
Number of sides of regular polygon
= 360/(20) = 18

Calculate the number of sides of a regular polygon with exterior angle of 18°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (18)
Number of sides of regular polygon
= 360/(18) = 20

Calculate the number of sides of a regular polygon with exterior angle of 15°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (15)
Number of sides of regular polygon
= 360/(15) = 24

Calculate the number of sides of a regular polygon with exterior angle of 12°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (12)
Number of sides of regular polygon
= 360/(12) = 30

Calculate the number of sides of a regular polygon with exterior angle of 10°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (10)
Number of sides of regular polygon
= 360/(10) = 36

Calculate the number of sides of a regular polygon with exterior angle of 9°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (9)
Number of sides of regular polygon
= 360/(9) = 40

Calculate the number of sides of a regular polygon with exterior angle of 6°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (6)
Number of sides of regular polygon
= 360/(6) = 60

Calculate the number of sides of a regular polygon with exterior angle of 5°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (5)
Number of sides of regular polygon
= 360/(5) = 72

Calculate the number of sides of a regular polygon with exterior angle of 4°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (4)
Number of sides of regular polygon
= 360/(4) = 90

Calculate the number of sides of a regular polygon with exterior angle of 3°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (3)
Number of sides of regular polygon
= 360/(3) = 120

Calculate the number of sides of a regular polygon with exterior angle of 2°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (2)
Number of sides of regular polygon
= 360/(2) = 180

Calculate the number of sides of a regular polygon with exterior angle of 1°
Number of sides of regular polygon
= 360/(exterior angle)
Exterior angle = (1)
Number of sides of regular polygon
= 360/(1) = 360

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