2007 AMC 12B Problem 3

The point O is the center of the circle circumscribed about triangle ABC, with \angle BOC = 120^{\circ} and \angle AOB = 140^{\circ}, as shown. What is the degree measure of \angle ABC?

\mathrm {(A)} 35\qquad \mathrm {(B)} 40\qquad \mathrm {(C)} 45\qquad \mathrm {(D)} 50\qquad \mathrm {(E)} 60

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.