Question

Find the measure of each exterior angles of a regular polygon which has:a) 12 sides ,b)15 sides
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Answer 1

use the formula ext angle = 360/n

Derivation

In any polygon sum of all the interior angles is given by 180(n−2) where n is the number of sides of the polygon and each angle of a regular polygon is given by 180(n−2)/n

measure of ext angle = 180 - int angle

interior angle of a regular polygon is given by 180(n−2)/n

=>=> measure of ext angle =180−(180(n−2))/n

=(180n−180n+360)/n

=360/n

When n=12

Exterior angle =360/12=30

n=15

Exterior angle=360/15=24