Let's analyze the provided figure to determine the following:

(a) One pair of vertical angles:

Vertical angles are opposite angles formed by the intersection of two lines. From the figure:

• A valid pair of vertical angles is ∠1 and ∠3, as they are directly opposite each other where lines $l$ and $m$ intersect.

(b) One pair of angles that form a linear pair:

A linear pair consists of two adjacent angles whose measures add up to $180^\circ$. From the figure:

• ∠3 and ∠4 form a linear pair, as they are adjacent and lie on the straight line $m$.

(c) One pair of angles that are supplementary:

Supplementary angles have measures that add up to $180^\circ$. This includes both linear pairs and non-adjacent angles that satisfy the condition. From the figure:

• ∠7 and ∠8 are supplementary because they lie on the straight line $n$.

Final Answers:

• (a) Vertical angles: ∠1 and ∠3.
• (b) Linear pair: ∠3 and ∠4.
• (c) Supplementary angles: ∠7 and ∠8.

Would you like further clarification or examples? Here are some related questions for deeper understanding:

1. How do we mathematically prove two angles are vertical or supplementary?
2. Can two obtuse angles ever form a linear pair? Why or why not?
3. What happens if vertical angles are not equal? Is it geometrically possible?
4. Can non-adjacent angles on intersecting lines be supplementary?
5. How are complementary angles different from supplementary angles?

Tip:

Remember, vertical angles are always equal, and supplementary angles can exist even if they are not adjacent!