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# Polygon

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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

#1
+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
+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

ElectricPavlov Apr 19, 2021