 # Number of sidesName of polygon 3triangle 4quadrilateral 5pentagon 6hexagon 7heptagon 8octagon 9nonagon 10decagon A polygon is a shape enclosed by straight.

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Number of sidesName of polygon 3triangle 4quadrilateral 5pentagon 6hexagon 7heptagon 8octagon 9nonagon 10decagon A polygon is a shape enclosed by straight lines.

TRIANGLE QUADRILATERAL PENTAGON HEXAGON sum of interior angles = 180° sum of interior angles = 2 x 180° = 360° = 4 x 180° = 720° = 3 x 180° = 540°

An n -sided polygon can be split into ( n – 2) triangles. The sum of the interior angles in an n -sided polygon = ( n – 2) x 180° The sum of the interior angles in an n -sided polygon = ( n – 2) x 180° Example Find the sum of the interior angles in a nonagon. Sum of interior angles = ( n – 2) x 180° = 7 x 180° = 1260° = (9 – 2) x 180°

Example Find the value of x. 105° 107° 140° 75° x Sum of interior angles = (5 – 2) x 180° = 540° x + 75 + 105 + 107 + 140 = 540 x + 427 = 540 x = 113°

 All the sides are the same length AND  All the angles are the same size

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INTERIOR ANGLE EXTERIOR ANGLE

60° 120° Sum of exterior angles = 360° Exterior angle = 360° ÷ 6 = 60° Interior angle = 180° – 60° = 120° Regular hexagon

72° 108° Sum of exterior angles = 360° Exterior angle = 360° ÷ 5 = 7° Interior angle = 180° – 72° = 108° Regular pentagon

45° 135° Sum of exterior angles = 360° Exterior angle = 360° ÷ 8 = 45° Interior angle = 180° – 45° = 135° Regular octagon

In a regular n -sided polygon: Exterior angle = Interior angle = Example The interior angle of a regular polygon is 156°. How many sides does the polygon have? Interior angle = The polygon has 15 sides.

72° Example ABCDE is a regular pentagon. Find the size of angle x. x A B C D E F Angle AEF = exterior angle = 360 ÷ 5 = 72° Angle EAF = 72° x = 180 – (72 + 72) = 36°

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