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:
[tex]a = \frac{180(n - 2)}{n}[/tex]
We have to solve the equation for "n"
Rearrange the equation
[tex]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}[/tex]
Thus the numerator of the fraction is -360
