The measures of the interior angles of a convex 9-gon form an arithmetic sequence and, measured in degrees, are all distinct integers. What is the measure of the largest possible angle if the smallest angle is 100 degrees?
The interior angles sum to 180 (9 -2) = 1260°
So
100 + (100 + d) + (100 +2d) + (100 + 3d) +(100 + 4d) + (100 + 5d) + (100 + 6d) + (100 + 7d) +
(100 + 8d) = 1260
900 + 36d = 1260
36d = 360
d = 10
Largest angle = 100 + 8 (10) = 180°
