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Pentagon Equilateral Hexagon Triangle Square Heptagon Octagon Enneagon

A 9–sided polygon is split into 7 triangles
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° © T Madas

What is the sum of the interior angles of a polygon with n sides?
What is the sum of the interior angles of this enneagon? A n - sided polygon can be split into triangles n – 2 © T Madas

sum of the interior angles of various polygons
triangle quadrilateral pentagon 180° 180° x 2 = 360° 180° x 3 = 540° hexagon heptagon octagon 180° x 4 = 720° 180° x 5 = 900° 180° x 6 = 1080° © T Madas

Consider the following polygon

Consider the following polygon

Consider the following polygon

Consider the following polygon

Consider the following polygon

Consider the following polygon

Consider the following polygon

Consider the following polygon

Consider the following polygon

Consider the following polygon

The central angle of a regular polygon
How do we find the central angle of a regular polygon with n sides? Central Angle 360° Central angle = n Central Angle © T Madas

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 © T Madas

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 © T Madas

The exterior angle of a regular pentagon
360° exterior angle = = 72° 5 The exterior angles of any polygon add up to 360° © T Madas

The exterior angle of a regular octagon
360° exterior angle = = 45° 8 The exterior angles of any polygon add up to 360° © T Madas

The interior angle of a regular polygon
A n - sided polygon can be split into triangles n – 2 © T Madas

the interior angles of various regular polygons
equilateral triangle square pentagon 180° x 2 = 360° 180° x 3 = 540° 180° ÷ 3 = 60° 360° ÷ 4 = 90° 540° ÷ 5 = 72° hexagon heptagon octagon 180° x 4 = 720° 180° x 5 = 900° 180° x 6 = 1080° 720° ÷ 6 = 120° 900° ÷ 7 ≈ 128.6° 1080° ÷ 8 = 135° © T Madas

For every regular polygon
360° exterior angle = n 360° central angle = n 180(n – 2) interior angle = n These formulae are very easy to derive © T Madas