<em><u>Complete Question:</u></em>
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?
<em><u>Answer:</u></em>
The numerator of fraction is -360
<em><u>Solution:</u></em>
Given that,
<em><u>The equation represents the angle measures, a, in a regular n-sided polygon is:</u></em>
![a = \frac{180(n - 2)}{n}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B180%28n%20-%202%29%7D%7Bn%7D)
We have to solve the equation for "n"
Rearrange the equation
![a \times n = 180(n - 2)\\\\a \times n = 180n - 360\\\\an - 180 n = -360\\\\Take\ n\ as\ common\ factor\\\\n(a-180) = -360\\\\n = \frac{-360}{a - 180}](https://tex.z-dn.net/?f=a%20%5Ctimes%20n%20%3D%20180%28n%20-%202%29%5C%5C%5C%5Ca%20%5Ctimes%20n%20%3D%20180n%20-%20360%5C%5C%5C%5Can%20-%20180%20n%20%3D%20-360%5C%5C%5C%5CTake%5C%20n%5C%20as%5C%20common%5C%20factor%5C%5C%5C%5Cn%28a-180%29%20%3D%20-360%5C%5C%5C%5Cn%20%3D%20%5Cfrac%7B-360%7D%7Ba%20-%20180%7D)
Thus the numerator of the fraction is -360
Answer:
12
Step-by-step explanation:
51 ÷ 3 = 17
204 ÷ 17 = 12
hope this helps