+977 In a certain regular polygon, the measure of each interior angle is $2$ times the measure of each exterior angle. Find the number of sides in this regular polygon.
+1950 We can write an equation.
The measure of an interior angle is (n−2)(180∘)/n where n is the sidelengths. Since, the exterior angle is 180 minues the interior angle, we have
(n−2)(180)/n=2·(180−(n−2)(180)/n)(n−2)(180)/n=360−2·(n−2)(180)/n)3·(n−2)(180)/n)=360(n−2)(180)/n=120(n−2)/n=2/3n−2=2n/33n−6=2nn=6
So our answer is 6.
We can check our work.
A 6-sided polygon has an interior of 120 and exterior of 60.
Thank! :)
+1950 We can write an equation.
The measure of an interior angle is (n−2)(180∘)/n where n is the sidelengths. Since, the exterior angle is 180 minues the interior angle, we have
(n−2)(180)/n=2·(180−(n−2)(180)/n)(n−2)(180)/n=360−2·(n−2)(180)/n)3·(n−2)(180)/n)=360(n−2)(180)/n=120(n−2)/n=2/3n−2=2n/33n−6=2nn=6
So our answer is 6.
We can check our work.
A 6-sided polygon has an interior of 120 and exterior of 60.
Thank! :)
