+585 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.
+1365 We can write an equation.
The measure of an interior angle is \( (n - 2)(180^\circ) / n \) where n is the sidelengths. Since, the exterior angle is 180 minues the interior angle, we have
\( (n - 2)(180) / n = 2 · ( 180 - (n - 2)(180) / n ) \\ (n - 2)(180) / n = 360 - 2 · (n - 2)(180) / n ) \\ 3 · (n - 2)(180) / n ) = 360 \\(n-2)(180)/n=120 \\(n-2)/n=2/3 \\n-2=2n/3 \\3n-6=2n \\n=6\)
So our answer is 6.
We can check our work.
A 6-sided polygon has an interior of 120 and exterior of 60.
Thank! :)
+1365 We can write an equation.
The measure of an interior angle is \( (n - 2)(180^\circ) / n \) where n is the sidelengths. Since, the exterior angle is 180 minues the interior angle, we have
\( (n - 2)(180) / n = 2 · ( 180 - (n - 2)(180) / n ) \\ (n - 2)(180) / n = 360 - 2 · (n - 2)(180) / n ) \\ 3 · (n - 2)(180) / n ) = 360 \\(n-2)(180)/n=120 \\(n-2)/n=2/3 \\n-2=2n/3 \\3n-6=2n \\n=6\)
So our answer is 6.
We can check our work.
A 6-sided polygon has an interior of 120 and exterior of 60.
Thank! :)
