Question 485890
The sum of the angles in a convex 9-gon is 7(180) = 1260. Hence the middle term is 1260/9 = 140 (the median of the angle measures). We can fix the smallest angle to be the smallest integer greater than 90, such that all the other angle measures are integers.


If a1 is the smallest angle, a5 = 140 and a9 is the largest angle, then we have an arithmetic sequence


a1 _ _ _ a5 _ _ _ a9


In other words, a5 = 140 = a1 + 4d. The optimal value of d is therefore 12, a1 = 140 - 4(12) = 92. The measure of a9 is 92 + 8(12) = 92 + 96 = 188 (degrees).