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

-360

Explanation:

Given:

`a = (180(n - 2))/(n)`

Solve for n. Multiply both sides by n

`a*n = (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 = (-360)/(a - 180)`

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