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the equation a= 180(n-2)/n 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?

Respuesta :

Banabanana
[tex]a= \frac{180(n-2)}{n} \\ an=180n-360 \\ an-180n=-360 \\ n(a-180)=-360 \\ n= \frac{-360}{a-180} [/tex]

numerator of the fraction is -360.

Answer:

-360.

Step-by-step explanation:

We have been give an equation [tex]a=\frac{ 180(n-2)}{n}[/tex], which represents the angle measures, a, in a regular n-sided polygon. We are asked to find the numerator of the fraction, while solving our equation for n.

Let us multiply both sides of our equation by n.

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

[tex]a*n= 180(n-2)[/tex]

Upon distributing 180 we will get,

[tex]a*n= 180n-360[/tex]

Let us subtract 180n to both sides of our equation.

[tex]a*n-180n= 180n-180n-360[/tex]

[tex]a*n-180n=-360[/tex]

Let us factor out n from left hand side of our equation.

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

Let us divide both sides of our equation by a-180.

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

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

Therefore, the numerator of our fraction with a denominator of (a-180) will be -360.  

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