Question

Solving for an Unknown Using the Distributive Property

Answer 1

Complete Question:

The equation a= 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:

The numerator of fraction is -360

Solution:

Given that,

The equation represents the angle measures, a, in a regular n-sided polygon is:

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

We have to solve the equation for "n"

Rearrange the equation

$a \times n = 180(n - 2)\\\\a \times n = 180n - 360\\\\an - 180 n = -360\\\\Take\ n\ as\ common\ factor\\\\n(a-180) = -360\\\\n = \frac{-360}{a - 180}$

Thus the numerator of the fraction is -360