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?
o n = d/180 + 2
o n = d/180 - 2
o n = d - 178
o n = d - 182

Explanation:

Step1: Start with Janelle's equation

Given $n = \frac{D + 360}{180}$, use the rule of fraction addition $\frac{a + b}{c}=\frac{a}{c}+\frac{b}{c}$. Here $a = D$, $b = 360$, $c = 180$.
$n=\frac{D}{180}+\frac{360}{180}$

Step2: Simplify the second - fraction

Since $\frac{360}{180}=2$, we have:
$n=\frac{D}{180}+2$

Answer:

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