Question

The sum of the angle measures of a polygon with n sides is 2880.find n

Answer 1

18 sides

Explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here sum = 2880°, thus

180° (n - 2) = 2880 ( divide both sides by 180 )

n - 2 = 16 ( add 2 to both sides )

n = 18

Answer 2

The number of sides of the polygon is 18.

Explanation:

Given,

The sum of interior angles of a polygon is 2880°

To find the number of sides of the polygon.

Formula

The sum of the interior angle of n side polygon is (n-2)×180°

According to the problem,

(n-2)×180° = 2880°

or, n-2 =
`(2880)/(180)`

or, n-2 = 16

or, n = 18

Hence,

The number of sides of the polygon is 18.