polygons - Grade 8 Mathematics- classification
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- 2. © T Madas Equilateral Triangle Square Pentagon Hexagon Heptagon Octagon Enneagon Decagon Hendecagon Dodecagon
- 3. © T Madas 20 sides Eicosagon
- 4. © T Madas 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
- 5. © T Madas 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
- 6. © T Madas sum of the interior angles of various polygons triangle 180° quadrilateral 180° x 2 = 360° pentagon 180° x 3 = 540° hexagon 180° x 4 = 720° heptagon 180° x 5 = 900° octagon 180° x 6 = 1080°
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- 8. © T Madas Consider the following polygon What do the exterior angles of a polygon add up to? Exterior Angle
- 9. © T Madas 360° Consider the following polygon What do the exterior angles of a polygon add up to?
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- 11. © T Madas Exterior Angle Consider the following polygon What do the exterior angles of a polygon add up to?
- 12. © T Madas Consider the following polygon What do the exterior angles of a polygon add up to?
- 13. © T Madas Consider the following polygon What do the exterior angles of a polygon add up to?
- 14. © T Madas Consider the following polygon What do the exterior angles of a polygon add up to?
- 15. © T Madas Consider the following polygon What do the exterior angles of a polygon add up to?
- 16. © T Madas Consider the following polygon What do the exterior angles of a polygon add up to?
- 17. © T Madas Consider the following polygon What do the exterior angles of a polygon add up to?
- 18. © T Madas Consider the following polygon 360° What do the exterior angles of a polygon add up to?
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- 20. © 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
- 21. © 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° 5 = 72°
- 22. © 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° 8 = 45°
- 23. © T Madas The exterior angle of a regular pentagon exterior angle = 360° 5 The exterior angles of any polygon add up to 360° = 72°
- 24. © T Madas The exterior angle of a regular octagon exterior angle = 360° 8 = 45° The exterior angles of any polygon add up to 360°
- 25. © T Madas 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
- 26. © T Madas the interior angles of various regular polygons equilateral triangle 180° square 180° x 2 = 360° pentagon 180° x 3 = 540° hexagon 180° x 4 = 720° heptagon 180° x 5 = 900° octagon 180° x 6 = 1080° ÷ 3 = 60° 360° ÷ 4 = 90° 540° ÷ 5 = 72° 720° ÷ 6 = 120° 900° ÷ 7 ≈ 128.6° 1080° ÷ 8 = 135°
- 27. © T Madas 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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