Question

The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s = 180(n – 2), where n is the number of sides. Benita solves this equation for n and writes the equivalent equation n = + 2. Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°?

Answer 1

1,260=180(n-2)
1260/180=n-2
7=n-2
n=9
it has nine sides, hope it helps

Answer 2

Equivalent equation of
`s =180(n-2)` is
`n =(s)/(180)+2`

And the number of sides does a polygon have is, n =9.

Explanation:

Given:

The sum of the interior angles, 's' in a n-sided polygon can be determined

using the formula is:
`s =180(n-2)` .....[1]

where n is the number of sides.

We can write the equivalent equation of [1]

`s = 180(n-2)`

Divide both sides by 180;

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

Simplify:

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

Add 2 to both sides of an equation:

`(s)/(180)+2=n-2+2`

Simplify, we get;

`n =(s)/(180)+2` ......[2]

Now, to find the value of n ;

Given: s =1260°

Substitute this value in [2] we get;

`n =(1260)/(180)+2`

or

n = 7+2 =9

Therefore, the number of sides in a polygon is, n=9