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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?​

The equation a180n2n 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 o class=

Respuesta :

akposevictor

Answer:

-360

Step-by-step explanation:

Given:

[tex] a = \frac{180(n - 2)}{n} [/tex]

Solve for n. Multiply both sides by n

[tex] a*n = \frac{180(n - 2)}{n}*n [/tex]

[tex] an = 180(n - 2) [/tex]

Apply the distributive property

[tex] an = 180n - 360 [/tex]

Subtract 180n from both sides

[tex] an - 180n = - 360 [/tex]

Factor out n

[tex] n(a - 180) = - 360 [/tex]

Divide both sides by (a - 180)

[tex] n = \frac{-360}{a - 180} [/tex]

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

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