The ray OC stands on the straight line AOB so that ∠AOC = $4x$ and ∠BOC = $5x$. The ray OD bisects ∠AOC. What is the measure of ∠DOB?

∠AOC and ∠BOC form a linear pair, so $4x+5x=180$°, giving $x=20$°. Then ∠AOC = 80° and the bisector gives ∠AOD = 40°. A, O and B are collinear, so ∠DOB = 180° − ∠AOD = 180° − 40° = 140°. The trap 40° is ∠AOD itself, 100° is ∠BOC, and 130° comes from bisecting ∠BOC by mistake (180° − 50°).