Polygons
Index
Geometry
Polygons
 
 
Find / Calculate / Determine
The Exterior Angle Of A Regular Polygon
 
Find The Exterior Angle
Of A Regular Polygon With 18 Sides

Exterior angle regular polygon = 360/n
Regular 18-gon    n = (18)
Exterior angle regular 18-gon = 360/(18) = 20°

 
Find The Exterior Angle
Of A Regular Polygon With 15 Sides

Exterior angle regular polygon = 360/n
Regular 15-gon    n = (15)
Exterior angle regular 15-gon = 360/(15) = 24°

Use the introduction to relax and focus
 
 

Go to maths.com Polygons Index

Go to maths.com Home Page



How can we calculate
the size of the exterior angle
of a regular polygon?

Divide 360°
by the number of sides
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 size of the exterior angle
of a regular polygon?

360° ÷ number of sides
360/number of sides
360/n    where n = (number of sides)

Calculating The Exterior Angle
Of A Regular Polygon
Using The Formula
Exterior Angle = 360/n
where n = (number of sides)

Calculate exterior angle regular triangle
Exterior angle regular polygon = 360/n
Regular triangle    n = (3)
Exterior angle regular triangle
= 360/(3) = 120°

Calculate exterior angle regular quadrilateral
Exterior angle regular polygon = 360/n
Regular quadrilateral    n = (4)
Exterior angle regular quadrilateral
= 360/(4) = 90°

Calculate exterior angle regular pentagon
Exterior angle regular polygon = 360/n
Regular pentagon    n = (5)
Exterior angle regular pentagon
= 360/(5) = 72°

Calculate exterior angle regular hexagon
Exterior angle regular polygon = 360/n
Regular hexagon    n = (6)
Exterior angle regular hexagon
= 360/(6) = 60°

Calculate exterior angle regular heptagon
Exterior angle regular polygon = 360/n
Regular heptagon    n = (7)
Exterior angle regular heptagon
= 360/(7) = 51.4° (correct to 1 decimal place)

Calculate exterior angle regular octagon
Exterior angle regular polygon = 360/n
Regular octagon    n = (8)
Exterior angle regular octagon
= 360/(8) = 45°

Calculate exterior angle regular nonagon
Exterior angle regular polygon = 360/n
Regular nonagon    n = (9)
Exterior angle regular nonagon
= 360/(9) = 40°

Calculate exterior angle regular decagon
Exterior angle regular polygon = 360/n
Regular decagon    n = (10)
Exterior angle regular decagon
= 360/(10) = 36°

Calculate exterior angle regular dodecagon
Exterior angle regular polygon = 360/n
Regular dodecagon    n = (12)
Exterior angle regular dodecagon
= 360/(12) = 30°

We may also have
exterior angle n-gon [n sides]
examples
exterior angle 11-gon [11 sides]
exterior angle 29-gon [29 sides]
exterior angle 30-gon [30 sides]

Calculate exterior angle regular 11-gon
Exterior angle regular polygon = 360/n
Regular 11-gon    n = (11)
Exterior angle regular 11-gon
= 360/(11) = 32.7° (correct to 1 decimal place)

Calculate exterior angle regular 29-gon
Exterior angle regular polygon = 360/n
Regular 29-gon    n = (29)
Exterior angle regular 29-gon
= 360/(29) = 12.4° (correct to 1 decimal place)

Calculate exterior angle regular 30-gon
Exterior angle regular polygon = 360/n
Regular 30-gon    n = (30)
Exterior angle regular 30-gon
= 360/(30) = 12°

Copyright © maths.com 2005-2008 All Rights Reserved