1. **Problem statement:** We are given a circle with two chords intersecting inside it, forming four angles. One angle is 25°, another is 84°, and we need to find the unknown angle $x$ opposite the 84° angle inside the smaller triangle formed. 2. **Key rule:** When two chords intersect inside a circle, the opposite angles formed are supplementary, meaning their measures add up to 180°. 3. **Apply the rule:** Since $x$ and 84° are opposite angles formed by the intersecting chords, we have: $$x + 84^\circ = 180^\circ$$ 4. **Solve for $x$:** $$x = 180^\circ - 84^\circ = 96^\circ$$ 5. **Check the options:** None of the options match 96°, so let's consider the smaller triangle formed by the chords and the 25° angle. 6. **Triangle angle sum rule:** The sum of angles in a triangle is 180°. 7. **In the smaller triangle, the angles are:** 25°, 84°, and $x$. 8. **Calculate $x$:** $$x = 180^\circ - 84^\circ - 25^\circ = 71^\circ$$ 9. **Closest option:** A. $x = 70^\circ$ is the closest to 71°. **Final answer:** $x = 70^\circ$ (Option A)