Question

The equation a=180(n-2)/n represents the angle measures, a, ina 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

Answer:

-360

Step-by-step explanation:

Given:

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

Solve for n. Multiply both sides by n

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

$an = 180(n - 2)$

Apply the distributive property

$an = 180n - 360$

Subtract 180n from both sides

$an - 180n = - 360$

Factor out n

$n(a - 180) = - 360$

Divide both sides by (a - 180)

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

Therefore, the numerator of the fraction that n is equal to is -360