Question

The sum of the measures of the interior angles is 1,440 degrees. How many sides does the polygon have? 4 6 8 10

Answer 1

The equation to find the side number is:
(interior angle total/180)+2.
(1440/180)+2
8+2
10 sides

Answer 2

10 sides.

Explanation:

Given : The sum of the measures of the interior angles is 1,440 degrees.

To Find: How many sides does the polygon have?

Solution:

Let n be the number of sides .

Formula :
`(n-2) * 180^(\circ) =\text{Sum of all interior angles}`

We are given that The sum of the measures of the interior angles is 1,440 degrees.

Substitute the value sin the formula .

`(n-2) * 180^(\circ) =1440`

`(n-2) =(1440)/(180)`

`(n-2) =8`

`n=8+2`

`n=10`

Thus the polygon has 10 sides.