The problem asks which pair of angles must be supplementary. Supplementary angles are two angles that add up to $180^\circ$.

Let's analyze the diagram and the options:

• Angles 2 and 3: These are adjacent angles on the same straight line (line $l$), meaning they form a linear pair. Linear pairs are always supplementary, as they add up to $180^\circ$.

• Angles 4 and 10: These are corresponding angles formed by transversals and parallel lines. Corresponding angles are equal, not supplementary.

• Angles 8 and 12: These are alternate interior angles. Alternate interior angles formed by parallel lines and a transversal are congruent, not supplementary.

• Angles 7 and 15: These are also alternate interior angles. As mentioned, alternate interior angles are congruent, not supplementary.

So, the correct pair of supplementary angles is Angles 2 and 3, which is the correct answer.

Would you like further details or have any questions?

Here are 5 related questions:

1. What are corresponding angles, and how are they formed?
2. Can two angles be supplementary if they are not adjacent?
3. What are alternate interior angles, and when are they congruent?
4. Why are linear pairs always supplementary?
5. How can we use the concept of vertical angles to solve similar problems?

Tip: Always remember that angles on a straight line (linear pairs) sum to 180°, making them supplementary by definition!