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hammer [34]
3 years ago
11

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?
Mathematics
2 answers:
Artyom0805 [142]3 years ago
7 0
a= \frac{180(n-2)}{n}  \\  an=180n-360  \\ an-180n=-360 \\ n(a-180)=-360 \\ n= \frac{-360}{a-180}

<span>numerator of the fraction is -360.</span>
Lostsunrise [7]3 years ago
4 0

Answer:

-360.

Step-by-step explanation:

We have been give an equation a=\frac{ 180(n-2)}{n}, 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.

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

a*n= 180(n-2)

Upon distributing 180 we will get,

a*n= 180n-360

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

a*n-180n= 180n-180n-360

a*n-180n=-360

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

n(a-180)=-360

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

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

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

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

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