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.
+37084 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
+37084 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
