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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.

 Apr 19, 2021

Best Answer 

 #1
avatar+33757 
+2

Sum of interior angles     (n-2)(180)

    then each interior angle      (n-2)(180) / n

       each exterior angle   is   180 - (n-2)(180)/n

 

Now to the question     (n-2)(180)/n     ={ 180 - (n-2)(180)/n  } *10

                                      (180n- 360)     ={ 180n - (n-2)(180) } * 10

                                       180n - 360      =  {180n - 180n + 360 } * 10

                                         180n -360   =  3600

                                          180 n = 3960

                                                n = 22                              interior angle = 163.636     exterior = 16.363

 

ANOTHER way:

10 n   + n = 180

n = 16.363   = exterior angle

10n = interior = 163.636

 

(n-2)(180)/n = 163.636

180n - 360 = 163.636 n

n = 22      

 Apr 19, 2021
 #1
avatar+33757 
+2
Best Answer

Sum of interior angles     (n-2)(180)

    then each interior angle      (n-2)(180) / n

       each exterior angle   is   180 - (n-2)(180)/n

 

Now to the question     (n-2)(180)/n     ={ 180 - (n-2)(180)/n  } *10

                                      (180n- 360)     ={ 180n - (n-2)(180) } * 10

                                       180n - 360      =  {180n - 180n + 360 } * 10

                                         180n -360   =  3600

                                          180 n = 3960

                                                n = 22                              interior angle = 163.636     exterior = 16.363

 

ANOTHER way:

10 n   + n = 180

n = 16.363   = exterior angle

10n = interior = 163.636

 

(n-2)(180)/n = 163.636

180n - 360 = 163.636 n

n = 22      

ElectricPavlov Apr 19, 2021

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