Question

the total number of degrees, d, in an n - sided polygon is given by the formula ( d = 180(n - 2) ). when janelle solves for n, she gets ( n=\frac{d + 360}{180} ). sophie solved the same equation for n and got an equivalent equation. which of the following could be sophies equation?
( n=\frac{d}{180}+2 )
( n=\frac{d}{180}-2 )
( n = d - 178 )
( n = d - 182 )

Explanation:

Step1: Start with the original formula

We have the formula for the total number of degrees \( D \) in an \( n \)-sided polygon: \( D = 180(n - 2) \). We need to solve for \( n \) and check which of the given options matches the equivalent equation.

Step2: Divide both sides by 180

To isolate the term with \( n \), we divide both sides of the equation \( D = 180(n - 2) \) by 180. This gives us:

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

Step3: Add 2 to both sides

Now, to solve for \( n \), we add 2 to both sides of the equation \( \frac{D}{180}=n - 2 \). This results in:

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

Answer:

\( n=\frac{D}{180}+2 \) (the first option among the given choices)