Question

which of the following best describes a regular polygon when the sum of its interior angles is 1080 degrees A.) octagon B.) heptagon C.) hexagon D.) nonagon

Answer 1

a) octagon

1080= (n-2)180
1080/180=6

6=(n-2)
n=8
(This is the formula for finding the sum of interior angles in polygons. n represents the number of sides in the polygon)

Answer 2

Option A is correct.

Explanation:

Given: Sum of all the interior angles of a regular polygon = 1080°

To find: number of sides or name of polygon.

We know that Sum of all interior angle of a regular polygon is given by following formula,

Sum of all angles = ( n - 2 ) × 180° , where n = no of sides.

⇒ 1080° = ( n - 2 ) × 180°

n - 2 = 6

n = 6 + 2

n = 8

Name of regular polygon is Regular Octagon.

Therefore, Option A is correct.