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

The equation a = \frac{180(n-2)}{n} can be rewritten as:

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

Multiplying both sides by n:

an = 180n - 360

Rearranging the equation:

an - 180n = -360

n(a - 180) = -360

Dividing both sides by (a - 180):

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

Therefore, the numerator of the fraction is -360.