Question

If the difference between the interior and exterior angle of a regular polygon is 100 degree,then the number of diagonals of the polygon is

Answer 1

Answer:

Diagonals = 27.

Step-by-step explanation:

interior angle = (n - 2)180/n

Exterior angle = 360/n

[(n - 2)180/n] - (360/n) = 100°

180n - 360/n - 360/n = 100°

180n - 720/n = 100°

180n - 720 = 100n

180n - 100n = 720

80n = 720

n = 9

So, this polygon is nonagon whose interior and exterior angle differ by 100°.

Diagonal in nonagon = n(n-3)/2

= 9(9 - 3)/2

= 9 * 6/2

= 54/2

= 27.