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 = (d + 360)/180. sophie solved the same equation for n and got an equivalent equation. which of the following could be sophies equation?
n=(d/180)+2
n=(d/180)-2
n = d - 178
n = d - 182

Explanation:

Step1: Start with Janelle's formula

Given $n=\frac{D + 360}{180}$.

Step2: Split the fraction

Using the rule $\frac{a + b}{c}=\frac{a}{c}+\frac{b}{c}$, we have $n=\frac{D}{180}+\frac{360}{180}$.

Step3: Simplify the second - fraction

Since $\frac{360}{180}=2$, then $n=\frac{D}{180}+2$.

Answer:

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