Math, asked by vk5544323, 9 months ago

Find the measure of each
exterior angle of a regular polygon of:
(1) 8 sides
(2) 12 sides

Answers

Answered by anju24c

we know that,

sum of all the interior angles = (no. of sides - 2) × 180

so, in an regular octagon(polygon with 8 sides)

sum of all the interior angles = (no. of sides - 2) × 180

= (8 - 2) × 180

= 6 × 180

= 1080

sum of all the interior angles of an octagon = 1080

measure of a single interior angle = sum of all the interior angles/total sides

= 1080/8

= 135

we know that an interior and an exterior angle of a regular polygon is always supplementary(supplementary means the two angle sums up to 180)

let the exterior angle be x

so, 135 + x = 180

⇒ x = 180 - 135

= 45

so, in a regular do-decagon(polygon with 12 sides)

sum of all the interior angles = (no. of sides - 2) × 180

= (12-2) × 180

= 10 × 180

= 1800

sum of all the interior angles of an do-decagon = 1800

measure of a single interior angle = 1800/12

= 150

let the exterior angle be y

so, 150 + y = 180

⇒ y = 180 - 150

= 30

exterior angle of a regular polygon of 8 sides = 45

exterior angle of a regular polygon of 12 sides = 30

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