Transcript polygons
© T Madas Equilateral Triangle Square Pentagon Heptagon Octagon Decagon Hendecagon Hexagon Enneagon Dodecagon © T Madas 20 sides Eicosagon © T Madas 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 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) © T Madas 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° © T Madas © T Madas Consider the following polygon Exterior Angle What do the exterior angles of a polygon add up to? © T Madas Consider the following polygon What do the exterior angles of a polygon add up to? 360° © T Madas © T Madas Consider the following polygon Exterior Angle What do the exterior angles of a polygon add up to? © T Madas Consider the following polygon What do the exterior angles of a polygon add up to? © T Madas Consider the following polygon What do the exterior angles of a polygon add up to? © T Madas Consider the following polygon What do the exterior angles of a polygon add up to? © T Madas Consider the following polygon What do the exterior angles of a polygon add up to? © T Madas Consider the following polygon What do the exterior angles of a polygon add up to? © T Madas Consider the following polygon What do the exterior angles of a polygon add up to? © T Madas Consider the following polygon What do the exterior angles of a polygon add up to? 360° © T Madas © 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 © 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 exterior angle = 360° = 72° 5 The exterior angles of any polygon add up to 360° © T Madas The exterior angle of a regular octagon exterior angle = 360° = 45° 8 The exterior angles of any polygon add up to 360° © T Madas 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) © T Madas 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° © T Madas 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 © T Madas © T Madas