The exterior angles of a k-sided polygon form an arithmetic sequence. The smallest and largest interior angles of the polygon are 136 degrees and 176 degrees . What is k?
Equating sums for the interior angles, we have that
( 136 +176) (k/2) = 180 (k - 2) simplify
(312)k/2 = 180k - 360
156k = 180k - 360
180k -156k = 360
24k = 360
k = 360 /24 = 15