+1286 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.
+37147 Interior angle + exterior angle = 180 degrees
23 e + e = 180
e = 7.5 degrees so interior angle = 172.5
Sum of interior angles of n-gon is ( n-2)*180
each angle is then (n-2)*180 / n and this equals 172.5 degrees solve for n
(n-2)*180 / n = 172.5
180n -360 = 172.5 n
n = 48 sides
Maybe a bit simpler to realize exterior angles sum to 360
n (7.5) = 360
n = 48 sides
+37147 User Bosco pointed out an error in my solution.....
Here is a correction
Interior angle + exterior angle = 180 degrees
2 e + e = 180
e = 60 degrees so interior angle = 120 degrees
Sum of interior angles of n-gon is ( n-2)*180
each angle is then (n-2)*180 / n and this equals 120 degrees solve for n
(n-2)*180 / n = 120
180n -360 = 120 n
n =6 sides
Maybe a bit simpler to realize exterior angles sum to 360
n (60) = 360
n = 6 sides
THANX , Bosco !!
