1. **State the problem:** We have two intersecting chords inside a circle creating four angles. One angle is 137°, the angle opposite it is $x$, and another angle adjacent to $x$ is 94°. We need to find the value of $x$. 2. **Formula used:** When two chords intersect inside a circle, the measure of each angle formed is half the sum of the measures of the arcs intercepted by the angle and its vertical opposite angle. This means opposite angles are equal. 3. **Important rule:** Opposite angles formed by two intersecting chords are equal. 4. **Apply the rule:** Since $x$ is opposite the angle measuring 137°, we have $$x = 137°$$ 5. **Conclusion:** The value of $x$ is 137°.