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Equilateral
Triangle
Square
Pentagon
Heptagon
Octagon
Decagon
Hendecagon
Hexagon
Enneagon
Dodecagon
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20 sides
Eicosagon
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What is the sum of the interior angles of this enneagon?
Interior Angle
A 9–sided polygon is split into 7 triangles
7 x 180° = 1260°
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What isisthe
thesum
sumofof
interior
angles
of enneagon?
a polygon
What
thethe
interior
angles
of this
with n sides?
A n - sided polygon can be split into n – 2
triangles
sum = (n - 2)´ 180° = 180(n - 2)
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sum of the interior angles of various polygons
triangle
180°
hexagon
180° x 4 = 720°
quadrilateral
180° x 2 = 360°
heptagon
180° x 5 = 900°
pentagon
180° x 3 = 540°
octagon
180° x 6 = 1080°
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© T Madas
Consider the following polygon
Exterior Angle
What do the exterior angles of a polygon add up to?
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Consider the following polygon
What do the exterior angles of a polygon add up to?
360°
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© T Madas
Consider the following polygon
Exterior Angle
What do the exterior angles of a polygon add up to?
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Consider the following polygon
What do the exterior angles of a polygon add up to?
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Consider the following polygon
What do the exterior angles of a polygon add up to?
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Consider the following polygon
What do the exterior angles of a polygon add up to?
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Consider the following polygon
What do the exterior angles of a polygon add up to?
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Consider the following polygon
What do the exterior angles of a polygon add up to?
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Consider the following polygon
What do the exterior angles of a polygon add up to?
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Consider the following polygon
What do the exterior angles of a polygon add up to?
360°
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© T Madas
The central angle of a regular polygon
How do we find the central
angle of a regular polygon
n sides?
Centralwith
Angle
Central angle =
360°
n
Central Angle
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The central angle of a regular polygon
How do we find the central
angle of a regular polygon
with n sides?
Central angle of a pentagon =
360°
= 72°
5
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The central angle of a regular polygon
How do we find the central
angle of a regular polygon
with n sides?
Central angle of an octagon =
360°
= 45°
8
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The exterior angle of a regular pentagon
exterior angle =
360°
= 72°
5
The exterior angles of any polygon add up to 360°
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The exterior angle of a regular octagon
exterior angle = 360° = 45°
8
The exterior angles of any polygon add up to 360°
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The interior angle of a regular polygon
Interior angle =
180(n – 2)
n
A n - sided polygon can be split into n – 2 triangles
sum = (n - 2)´ 180° = 180(n - 2)
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the interior angles of various regular polygons
equilateral
triangle
180° ÷ 3 = 60°
hexagon
180° x 4 = 720°
720° ÷ 6 = 120°
square
180° x 2 = 360°
360° ÷ 4 = 90°
heptagon
180° x 5 = 900°
900° ÷ 7 ≈ 128.6°
pentagon
180° x 3 = 540°
540° ÷ 5 = 72°
octagon
180° x 6 = 1080°
1080° ÷ 8 = 135°
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For every regular polygon
exterior angle =
central angle =
interior angle =
360°
n
360°
n
180(n – 2)
n
These formulae are very easy to derive
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© T Madas