The six interior angles of a convex hexagon are in arithmetic progression, and the smallest of them measures 100°. What does the largest one measure?

The interior angles of a hexagon add to (6 − 2) × 180° = 720°, so their average is 720/6 = 120°. In any arithmetic progression the average of the terms equals the average of the first and last, so (100 + L)/2 = 120 and L = 140°. The six angles are then 100°, 108°, 116°, 124°, 132° and 140°, which add to 720° and are all under 180°, so the hexagon really is convex. The trap 120° reports the average, which is the angle of a REGULAR hexagon and would need the progression to have no common difference at all; 160° comes from doubling the gap of 20°; and 130° halves it.