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2. Pentagon Equilateral Hexagon Triangle Square Heptagon Octagon Enneagon
Decagon
Hendecagon
Dodecagon
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3. 20 sides
Eicosagon
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4. 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°
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5. 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
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6. 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°
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8. Consider the following polygon
Exterior Angle
What do the exterior angles of a polygon add up to?
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9. Consider the following polygon
What do the exterior angles of a polygon add up to?
360°
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11. Consider the following polygon
Exterior Angle
What do the exterior angles of a polygon add up to?
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12. Consider the following polygon
What do the exterior angles of a polygon add up to?
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13. Consider the following polygon
What do the exterior angles of a polygon add up to?
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14. Consider the following polygon
What do the exterior angles of a polygon add up to?
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15. Consider the following polygon
What do the exterior angles of a polygon add up to?
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16. Consider the following polygon
What do the exterior angles of a polygon add up to?
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17. Consider the following polygon
What do the exterior angles of a polygon add up to?
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18. Consider the following polygon
What do the exterior angles of a polygon add up to?
360°
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20. 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
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21. 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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22. 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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23. The exterior angle of a regular pentagon
360°
exterior angle =
= 72° 5
The exterior angles of any polygon add up to
360°
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24. The exterior angle of a regular octagon
360°
exterior angle =
= 45° 8
The exterior angles of any polygon add up to
360°
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25. The interior angle of a regular polygon
A n - sided polygon can be split into triangles
n – 2
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26. 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°
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27. 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
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