maths.com - Geometry - Interior Angle Of A Regular Polygon

Geometry
Polygons

Find / Calculate / Determine
The Interior Angle Of A Regular Polygon

METHOD A
Step 1 Find The Exterior Angle
Step 2 Interior Angle = 180 - Exterior Angle
Examples using this method are in the column on the right

METHOD B
Step 1 Write Formula Interior Angle = 180(n - 2)/n
Step 2 Substitute The Number Of Sides For n
Examples using this method are shown in the videos below

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How can we calculate
the size of the interior angle
of a regular polygon?
Divide 360°
by the number of sides
of the regular polygon
to get the exterior angle
and then
subtract the exterior angle from 180°

Calculate interior angle of a regular pentagon
Exterior angle regular polygon = 360/n
Regular pentagon n = (5)
Exterior angle regular pentagon
= 360/(5) = 72°
Interior Angle Regular Polygon
= 180 - Exterior Angle
Interior Angle Regular Pentagon
= 180 - 72 = 108°

Calculate interior angle of a regular hexagon
Exterior angle regular polygon = 360/n
Regular hexagon n = (6)
Exterior angle regular hexagon
= 360/(6) = 60°
Interior Angle Regular Polygon
= 180 - Exterior Angle
Interior Angle Regular Hexagon
= 180 - 60 = 120°

Calculate interior angle regular octagon
Exterior angle regular polygon = 360/n
Regular octagon n = (8)
Exterior angle regular octagon
= 360/(8) = 45°
Interior Angle Regular Polygon
= 180 - Exterior Angle
Interior Angle Regular Octagon
= 180 - 45 = 135°

We may also have
interior angle n-gon [n sides]
examples
interior angle 20-gon [20 sides]
interior angle 30-gon [30 sides]
interior angle 36-gon [36 sides]

Calculate interior angle regular 20-gon
Exterior angle regular polygon = 360/n
Regular n-gon n = (20)
Exterior angle regular 20-gon
= 360/(20) = 18°
Interior Angle Regular Polygon
= 180 - Exterior Angle
Interior Angle Regular 20-gon
= 180 - 18 = 162°

Calculate interior angle regular 30-gon
Exterior angle regular polygon = 360/n
Regular 30-gon n = (30)
Exterior angle regular 30-gon
= 360/(30) = 12°
Interior Angle Regular Polygon
= 180 - Exterior Angle
Interior Angle Regular 30-gon
= 180 - 12 = 168°

Calculate interior angle regular 36-gon
Exterior angle regular polygon = 360/n
Regular 36-gon n = (36)
Exterior angle regular 36-gon
= 360/(36) = 10°
Interior Angle Regular Polygon
= 180 - Exterior Angle
Interior Angle Regular 30-gon
= 180 - 10 = 170°