Question

the difference between the interior and exterior angle of a regular polygon is 100 degrees. the number of sides in the polygon is:

Answer 1

Answer:

9

Step-by-step explanation:

interior angle of regular polygon = ((n - 2) × 180) / n

exterior angle of a regular polygon = 360/n

interior angle - exterior angle = 100

((n - 2) × 180) / n - (360 / n) = 100

(180n - 360) / n - (360 / n) = 100

(180n - 360 - 360) / n = 100

180n - 720 = 100n

(180n-360)/n - 360/n = 100

(180n-360-360)/n = 100 ( see the attachment to see how this values came)

180n - 100n = 720

80n = 720

n = 720/80

n = 9

∴ Number of sides, n = 9