Since the angles marked y° and u° are vertical angles, y=u. Subtracting the sides of y=u from the corresponding sides of x+y=u+w gives x=w. Since the angles marked w° and z° are vertical angles, w=z. Therefore, x=z, and so I must be true. The equation in II need not be true. For example, if x=w=z=t=70 and y=u=40, then all three pairs of vertical angles in the figure have equal measure and the given condition x+y=u+w holds. But it is not true in this case that y is equal to w. Therefore, II need not be true. Since the top three angles in the figure form a straight angle, it follows that x+y+z=180. Similarly, w+u+t=180, and so x+y+z=w+u+t. Subtracting the sides of the given equation x+y=u+w from the corresponding sides of x+y+z=w+u+t gives z=t. Therefore, III must be true. Since only I and III must be true, the correct answer is choice B. Choices A, C, and D are incorrect because each of these choices includes II, which need not be true.