Help?! Polygon question !! (1 Viewer)

[bubb]

What is the m sided polygon in terms of n, given each of its interior angles = 720/n ??
Steps?


The overall answer is m = 2n/ n-4?

 

[enigma_1]

We know that each angle is 720/n

Formula for each interior angle of polygon is 180(n-2)/n

The number of sides in the polygon are "m", so sub in m into the formula:

180(m-2)/m which is equivalent to 720/n each angle in the polygon

:. 180(m-2)/m = 720/n

divide both sides by 180

(m-2)/m=4/n

cross multiply

(m-n)n=4m

expand

mn-2n=4m

mn-4m=2n

factor out the "m"

m(n-4)=2n

:. m = 2n/(n-4)