Select the correct answer.
Given the following formula, solve for [tex]$n$[/tex].
[tex]$S=(n-2) 180$[/tex]
A. [tex]$n=\frac{S}{180}+2$[/tex]
B. [tex]$n=\frac{S+2}{180}$[/tex]
C. [tex]$n=\frac{S}{180}-2$[/tex]
D. [tex]$n=\frac{S-2}{180}$[/tex]
Answer (1)
Divide both sides of the equation by 180: 180 S = n − 2 .
Add 2 to both sides of the equation: 180 S + 2 = n .
The solution for n is: n = 180 S + 2 .
The correct answer is: n = 180 S + 2 .
Explanation
Understanding the Problem We are given the formula S = ( n − 2 ) 180 and asked to solve for n . This involves isolating n on one side of the equation.
Dividing by 180 First, we divide both sides of the equation by 180: 180 S = 180 ( n − 2 ) 180 180 S = n − 2
Adding 2 to Both Sides Next, we add 2 to both sides of the equation to isolate n : 180 S + 2 = n − 2 + 2 180 S + 2 = n
Final Solution Therefore, the solution for n is: n = 180 S + 2
Examples
This formula is used to find the number of sides of a polygon given the sum of its interior angles. For example, if the sum of the interior angles of a polygon is 540 degrees, we can use this formula to find the number of sides: n = 180 540 + 2 = 3 + 2 = 5 . Thus, the polygon has 5 sides (a pentagon). Understanding how to manipulate formulas like this is crucial in various fields, such as geometry, physics, and engineering, where you often need to rearrange equations to solve for specific variables.
