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

Answer:

Equivalent equation of  $s =180(n-2)$  is   $n =\frac{s}{180}+2$

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

Step-by-step 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;

$\frac{s}{180} =\frac{180(n-2)}{180}$

Simplify:

$\frac{s}{180}=n-2$

Add 2 to both sides of an equation:

$\frac{s}{180}+2=n-2+2$

Simplify, we get;

$n =\frac{s}{180}+2$                               ......[2]

Now, to find the value of n ;

Given: s =1260°

Substitute this value in [2] we get;

$n =\frac{1260}{180}+2$

or

n = 7+2 =9

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

Answer 2

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