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 ngon [n sides]
examples
exterior angle 11gon [11 sides]
exterior angle 29gon [29 sides]
exterior angle 30gon [30 sides]
Calculate exterior angle regular 11gon
Exterior angle regular polygon = 360/n
Regular 11gon n = (11)
Exterior angle regular 11gon
= 360/(11) = 32.7° (correct to 1 decimal place)
Calculate exterior angle regular 29gon
Exterior angle regular polygon = 360/n
Regular 29gon n = (29)
Exterior angle regular 29gon
= 360/(29) = 12.4° (correct to 1 decimal place)
Calculate exterior angle regular 30gon
Exterior angle regular polygon = 360/n
Regular 30gon n = (30)
Exterior angle regular 30gon
= 360/(30) = 12°
