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EquilateralTriangle

SquarePentagon Hexagon

Heptagon Octagon Enneagon

Decagon Hendecagon Dodecagon

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20 sides

Eicosagon

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Interior Angle

What is the sum of the interior angles of this enneagon?

7 x 180° =1260°

A 9–sided polygon is split into 7 triangles

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What is the sum of the interior angles of this enneagon?What is the sum of the interior angles of a polygon with n sides?

A n - sided polygon can be split into triangles

n – 2

( 2)n - 180´ ° 180( 2)n= -=sum

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sum of the interior angles of various polygons

triangle180°

quadrilateral180° x 2= 360°

pentagon180° x 3= 540°

hexagon180° x 4= 720°

heptagon180° x 5= 900°

octagon180° x 6= 1080°

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© T Madas

Consider the following polygon

What do the exterior angles of a polygon add up to?

Exterior Angle

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360°

Consider the following polygon

What do the exterior angles of a polygon add up to?

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© T Madas

Exterior Angle

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?

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Consider the following polygon

360°What do the exterior angles of a polygon add up to?

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© T Madas

Central Angle

Central Angle

The central angle of a regular polygon

How do we find the central angle of a regular polygon with n sides?

Central angle =360°

n

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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°5

= 72°

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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°8

= 45°

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The exterior angle of a regular pentagon

exterior angle =360°5

The exterior angles of any polygon add up to

360°

= 72°

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The exterior angle of a regular octagon

exterior angle = 360°8

= 45°

The exterior angles of any polygon add up to

360°

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The interior angle of a regular polygon

A n - sided polygon can be split into triangles

n – 2

( 2)n - 180´ ° 180( 2)n= -=sum

Interior angle =180(n – 2)

n

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the interior angles of various regular polygons

equilateraltriangle180°

square180° x 2= 360°

pentagon180° x 3= 540°

hexagon

180° x 4= 720°heptagon

180° x 5= 900°

octagon180° x 6= 1080°

÷ 3= 60° 360°÷ 4= 90° 540°÷ 5= 72°

720°÷ 6= 120° 900°÷ 7≈ 128.6° 1080°÷ 8= 135°

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central angle =360°

n

exterior angle =360°n

For every regular polygon

interior angle =180(n – 2)

n

These formulae are very easy to derive

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