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In a certain regular polygon, the measure of each interior angle is nine times the measure of each exterior angle. Find the number of sides in this regular polygon.

 Dec 1, 2020
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Measure of an interior angle =   (n-2)(180)  / n

Measure of an  exterior angle  =  (360)/n

 

Where n is the number of sides

 

So we have that

 

(9)(360)/n  = (n - 2) (180)/n      multiply through by n

 

(9)(360) =  (n - 2) (180)    simplify

 

3240 =  180n - 360

 

3240 + 360  = 180n

 

[3240 + 360 ]  / 180  =   n

 

20   =   n 

 

 

cool cool cool 

 Dec 1, 2020

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