The exterior angles of a k-sided polygon form an arithmetic sequence. The smallest and largest interior angles of the polygon are 136 and 144. What is k?
+37159 Smallest interior angle 136 exterior angle = 180 - 136 = 44 degrees
Largest interior angle 144 exterior angle = 180 -144 = 36 degrees
the exterior angles sum to 360
36 + 36 + d + 36 +2d + 36 + 3d + 36+4d + 36 + 5d + 36 + 6d + 36 + 7d + 44 = 360
8(36) + 28d + 44 = 360
d =1
k = 9
Interior angle sum:
(n-2)(180) = 7(180) =1260 1260 / 9 = 140 (the average) Check!
