1. **State the problem:** We are given a cyclic quadrilateral with an angle of 128° at point B on the circumference and need to find the angle $x$ at the center $O$ between chords $OA$ and $OC$. 2. **Recall the property:** In a cyclic quadrilateral, opposite angles add up to 180°. 3. **Apply the property:** Let the opposite angle to the 128° angle be $x$. Then, $$x + 128^\circ = 180^\circ$$ 4. **Solve for $x$:** $$x = 180^\circ - 128^\circ$$ $$x = 52^\circ$$ 5. **Conclusion:** The angle $x$ at the center $O$ is $52^\circ$. This uses the fundamental property of cyclic quadrilaterals that opposite angles sum to 180 degrees.