Question

the 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?

Explanation:

Step1: Cross - multiply

$a\times n=180(n - 2)$
$an = 180n-360$

Step2: Move terms with $n$ to one side

$an-180n=-360$

Step3: Factor out $n$

$n(a - 180)=-360$

Step4: Solve for $n$

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

Answer:

$-360$