1. The problem states that O is the center of the circle, and we have two angles: one at the circumference (angle A) as $2x + 10$ and one at the center (angle O) as $x + 110$. 2. Important rule: The angle at the center of a circle is twice the angle at the circumference subtended by the same arc. Mathematically, $$\text{angle at center} = 2 \times \text{angle at circumference}$$ 3. Using the given expressions, set up the equation: $$x + 110 = 2(2x + 10)$$ 4. Simplify the right side: $$x + 110 = 4x + 20$$ 5. Rearrange to isolate $x$: $$110 - 20 = 4x - x$$ $$90 = 3x$$ 6. Solve for $x$: $$x = \frac{90}{3} = 30$$ 7. Therefore, the value of $x$ is 30. Final answer: **30** (Option C)