1. **Problem:** Find the missing angle $x$ in a circle where the arc measures 110° and $x$ is the inscribed angle opposite the arc. 2. **Formula:** The inscribed angle theorem states that an inscribed angle is half the measure of its intercepted arc. 3. **Calculation:** $$x = \frac{110}{2}$$ 4. **Simplify:** $$x = 55^\circ$$ 5. **Explanation:** The inscribed angle $x$ is half the arc it intercepts, so $x$ equals 55°. Final answer: $x = 55^\circ$