Question

The sum of the interior angles of a polygon is 2160°. How many sides does this polygon
have?


PLEASE ANSWER WITH PROCEDURE ​

Answer 1

Question:

The sum of the interior angles of a polygon is 2160° . How many sides does this polygon have?

Step-by-step explanation:

we know general formula that,

sum of

interior angles of polygon = (no.of sides - 2) * 180°

so, let polygon have 'n' no. of sides then

2160° = (n - 2)*180°

(n - 2) = 2160 / 180

(n - 2) = 12

n = 12 + 2

n = 14

HENCE, THERE ARE 14 SIDES IN THE POLYGON.

Answer 2

Answer :-

14

Solution :-

Let the number of sides of the polygon be 'n'

Given

Sum of interior angles of a polygon ( S ) = 2160°

We are given to find the number of sides of the polygon

Relation between number of sides and sum of interior angles of a polygon

⇒ S = (n - 2) * 180°

Substituting the given values in relation

⇒ 2160° = (n - 2) * 180°

⇒ 2160/180 = n - 2

⇒ 12 = n - 2

⇒ 12 + 2 = n

⇒ 14 = n

⇒ n = 14

Therefore the given polygon have 14 sides.