1. **State the problem:** We are given a circle with points O, M, P, N on the circumference and Q as the center. Angles at O and P are 62° and 94° respectively. We need to solve for $x$, which is an angle related to the segments inside the circle. 2. **Identify the relevant theorem:** In a circle, the measure of an angle formed by two chords intersecting inside the circle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle. 3. **Apply the formula:** If two chords intersect inside a circle, the angle formed is $$x = \frac{1}{2}(\text{arc}_1 + \text{arc}_2)$$ where $\text{arc}_1$ and $\text{arc}_2$ are the measures of the arcs intercepted by the angle and its vertical angle. 4. **Use given angles:** The angles at O and P are 62° and 94°, which correspond to arcs intercepted by the chords. Since these are angles at the circumference, the arcs they intercept are twice these angles: $$\text{arc}_O = 2 \times 62° = 124°$$ $$\text{arc}_P = 2 \times 94° = 188°$$ 5. **Calculate $x$:** Using the formula for the angle formed by intersecting chords, $$x = \frac{1}{2}(124° + 188°) = \frac{1}{2}(312°) = 156°$$ 6. **Conclusion:** The value of $x$ is 156°.