Question

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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: Start with the given equation

$a=\frac{180(n - 2)}{n}$

Step2: Cross - multiply

$an=180(n - 2)$

Step3: Expand the right - hand side

$an = 180n-360$

Step4: Move all terms with $n$ to one side

$an-180n=- 360$

Step5: Factor out $n$

$n(a - 180)=-360$

Step6: Solve for $n$

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

Answer:

$-360$