1. **Problem Statement:** Given that lines BA and DC are parallel, identify the type of angle pair formed by \(\angle 1\) and \(\angle 4\), and determine if they are congruent or supplementary. 2. **Relevant Concepts:** When two parallel lines are cut by a transversal, several angle relationships arise: - Corresponding angles are congruent. - Alternate interior angles are congruent. - Alternate exterior angles are congruent. - Consecutive interior angles (same side interior) are supplementary. 3. **Identify the Angles:** \(\angle 1\) and \(\angle 4\) are on opposite sides of the transversal and outside the parallel lines BA and DC. 4. **Type of Angles:** Since they are on opposite sides of the transversal and outside the parallel lines, \(\angle 1\) and \(\angle 4\) are **alternate exterior angles**. 5. **Angle Relationship:** Alternate exterior angles are congruent when the lines are parallel. 6. **Conclusion:** \(\angle 1\) and \(\angle 4\) are alternate exterior angles and are congruent. **Final answer:** \(\angle 1\) and \(\angle 4\) are alternate exterior angles and are congruent.