Question: Give us that ray $BA$ is parallel to ray $DC$. You need to select which type of angle this pair is and then tell whether it's congruent or supplementary and the pair is angle one and angle 4.

1. **Problem Statement:** We are given that ray $BA$ is parallel to ray $DC$ and asked to identify the type of angle pair formed by angle 1 and angle 4, and whether they are congruent or supplementary. 2. **Understanding the Setup:** When two rays (or lines) are parallel, angles formed by a transversal crossing these rays have special relationships. 3. **Types of Angle Pairs:** Common angle pairs with parallel lines include corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. 4. **Identifying the Angle Pair:** Angles 1 and 4 are typically positioned such that they are alternate exterior angles when rays $BA$ and $DC$ are parallel. 5. **Angle Relationship Rule:** Alternate exterior angles formed by a transversal with two parallel lines are congruent. 6. **Conclusion:** Therefore, angle 1 and angle 4 are alternate exterior angles and they are congruent. **Final answer:** Angle 1 and angle 4 are alternate exterior angles and they are congruent.