I have opened the image you uploaded. Let's proceed by identifying the relationships between the pairs of angles:

1. ∠3 and ∠12: These angles are on the same side of the transversal and outside the two lines. Therefore, they are Same-side exterior angles.

2. ∠3 and ∠11: These angles are in corresponding positions with respect to the two lines and the transversal, making them Corresponding angles.

3. ∠9 and ∠2: These angles lie on opposite sides of the transversal but outside the two lines, so they are Alternate exterior angles.

4. ∠2 and ∠12: These angles lie inside the two lines and on opposite sides of the transversal, meaning they are Alternate interior angles.

5. ∠4 and ∠8: These angles form a linear pair, meaning they are Linear pair.

6. ∠2 and ∠4: These angles are vertically opposite each other, making them Vertical angles.

7. ∠4 and ∠1: These two angles have no special relationship, so the answer is No relation.

Would you like further clarification on any of these angle relationships? Here are some related questions to expand your understanding:

1. What are alternate interior angles, and when do they occur?
2. How do same-side exterior angles help determine parallel lines?
3. Can vertical angles ever be unequal?
4. How do linear pairs relate to supplementary angles?
5. In what situations do corresponding angles occur?

Tip: Always remember that vertical angles are congruent, meaning they are always equal in measure.