Question

The sum of the angle measures of a polygon with n sides is given find n1440

Answer 1

Given in the question:

a.) The sum of all angles of a polygon is 1,440 degrees.

To be able to determine what polygon has a total sum of angles of 1,440 degrees, we will be using the following formula:

`\text{ }\Theta=(n-2)x180^(\circ)`

We get,

`\text{ 1},440^(\circ)=(n-2)x180^(\circ)`
`\text{ 1},440^(\circ)=180n-360^(\circ)`
`180n=1,440^(\circ)\text{ + 360}^(\circ)`
`180n=1,800^(\circ)`
`(180n)/(180)=(1,800^(\circ))/(180)`
`n\text{ = 10}`

Therefore, that polygon is a decagon or a polygon with 10 sides.