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The result of dividing the interior angles of a regular polygon by its exterior angle is 2.5, find the number of sides of the polygon​

 Jun 9, 2022
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Let the measure of one interior angle = x

And its exterior angle = 180  - x

 

So

 

x / ( 180 - x)  = 2.5

 

x = 2.5 (180 - x)

 

x = 450 - 2.5x

 

x + 2.5x =  450

 

3.5x  =  450

 

x =  450 / 3.5  =  the measure of an exterior angle

 

The  number of sides is given by

 

(N - 2) (180) / N  =   450/ 3.5        simplify

 

180N - 360 =   (450 / 3.5) N

 

180N - (450/3.5) N  =  360

 

(630 - 450) N   =   360 * 3.5

 

180N  =  1260

 

N  = 1260 / 180  =    7   =  the number of sides

 

 

cool cool cool

 Jun 9, 2022

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