Question

The equation a = a equals StartFraction 180 left-parenthesis n minus 2 right-parenthesis Over n EndFraction. 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 1

Start with a = 180(n − 2)/n. Multiply both sides by n: an = 180n − 360. Rearranging gives n(a − 180) = −360, so n = −360/(a − 180).

Thus the numerator is −360.