1. **State the problem:** We have a circle with center O and an inscribed triangle ABC. The central angle $\angle AOB = 160^\circ$ and we need to find the inscribed angle $x = \angle ACB$. 2. **Recall the rule:** The inscribed angle subtending the same arc as a central angle is half the measure of the central angle. 3. **Apply the formula:** $$x = \frac{1}{2} \times \angle AOB$$ 4. **Substitute the given value:** $$x = \frac{1}{2} \times 160^\circ$$ 5. **Calculate:** $$x = 80^\circ$$ 6. **Conclusion:** The inscribed angle $x$ is $80^\circ$.