Question

solving for an unknown using the distributive property

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:

Clear the fraction

Using the Literal Equations and Algebraic Rearrangement knowledge points

$$
LATEXBLOCK0
$$

Expand the expression

Using the Distributive Property knowledge point

$$ an = 180n - 360 $$

Group terms with n

Using the Algebraic Rearrangement knowledge point

$$
LATEXBLOCK1
$$

Solve for n

Using the Algebraic Rearrangement knowledge point

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

Answer:

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? <blank>\(-360\)</blank>