1. **State the problem:** Determine the relationship between angles $\angle 7$ and $\angle 3$ formed by two parallel lines intersected by two transversals. 2. **Recall relevant theorems:** - Corresponding Angles Theorem: Corresponding angles are congruent. - Consecutive Interior Angles Theorem: Consecutive interior angles are supplementary. - Alternate Exterior Angles Theorem: Alternate exterior angles are congruent. 3. **Analyze the position of $\angle 7$ and $\angle 3$:** - $\angle 7$ and $\angle 3$ lie on opposite sides of the transversal and outside the parallel lines. 4. **Apply the Alternate Exterior Angles Theorem:** - Since $\angle 7$ and $\angle 3$ are alternate exterior angles formed by parallel lines and a transversal, they are congruent. 5. **Conclusion:** - $\angle 7 \cong \angle 3$ by the Alternate Exterior Angles Theorem. **Final answer:** $$\angle 7 = \angle 3$$