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Mary draws an equiangular polygon with m sides, and George draws an equiangular polygon with g sides, where m is less than g. If the exterior angle of Mary's polygon is congruent to the interior angle of George's polygon, find g. 

 

help, anyone???

 Jan 14, 2019
edited by Guest  Jan 14, 2019
 #1
avatar+57 
+2

It says, that the exterior angle of a polygon with m sides is equal to a regular polygon with g sides. So,

 

\(\frac{360}{m} = \frac{180(g + 2)}{g}\)

\(360g = 180gm + 360m\)

\(2g = gm + 2m\)

Factoring out g:

\(2g - gm = 2m\)

\(g(2-m) = 2m\)

 

So therefore, \(g = \frac{2m}{2-m}\).

 

-24

 Jan 15, 2019
 #2
avatar+101431 
+1

Exterior angle of Mary's polygon =    360 / m

 

Interior angle of George's polygon  =   (g - 2)*180 / g

 

Since these are congruent....then

 

360 / m  =   (g - 2)  * 180 / g         cross - multiply

 

360g  =  180m * (g - 2)

 

360g = 180 gm - 360m

 

360m  = 180gm - 360g

 

2m = gm - 2g

 

2m =   g ( m - 2 )

 

g =  2m / ( m - 2)

 

 

cool cool cool

 Jan 15, 2019

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