solving for an unknown using the distributive property\nthe equation $a = \\frac{180(n - 2)}{n}$ represents…

solving for an unknown using the distributive property\nthe equation $a = \\frac{180(n - 2)}{n}$ represents the angle measures, $a$, in a regular n - sided polygon. when the equation is solved for $n$, $n$ is equal to a fraction with a denominator of $a - 180$. what is the numerator of the fraction?

solving for an unknown using the distributive property\nthe equation $a = \\frac{180(n - 2)}{n}$ represents the angle measures, $a$, in a regular n - sided polygon. when the equation is solved for $n$, $n$ is equal to a fraction with a denominator of $a - 180$. what is the numerator of the fraction?

Answer

Answer:

$- 360$

Explanation:

Step1: Cross - multiply

$an = 180(n - 2)$

Step2: Expand the right - hand side

$an=180n - 360$

Step3: Move terms with $n$ to one side

$an-180n=-360$

Step4: Factor out $n$

$n(a - 180)=-360$

Step5: Solve for $n$

$n=\frac{-360}{a - 180}$