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

 Jun 18, 2021
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Measure of  each interior angle  =  ( n - 2) *180  / 2

 

Measure of  each exterior angle =  360  / n

 

So

 

(n  - 2) 180  /  n      =  10  [  360  / n ]              {  divide out  n  }

 

(n -2)  180  =   3600

 

180n   -  360    = 3600

 

180n   =   3600  +  360

 

180n  =  3960

 

n =  22 sides

 

 

cool cool cool

 Jun 18, 2021
edited by CPhill  Jun 18, 2021

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