Question

one pair of angles that form a linear pair
one pair of angles that are supplementary

(i) vertical angles: ∠□ and ∠□
(ii) linear pair: ∠□ and ∠□
(iii) supplementary angles: ∠□ and ∠□

Explanation:

(i) Vertical Angles

Vertical angles are opposite angles formed by two intersecting lines. For example, ∠1 and ∠4 are vertical angles (or ∠2 and ∠3, ∠5 and ∠8, ∠6 and ∠7). Let's take ∠1 and ∠4. When two lines intersect, the vertical angles are equal. So ∠1 and ∠4 are vertical angles.

A linear pair of angles are adjacent angles that form a straight line (sum to 180°). For example, ∠1 and ∠2. They are adjacent and form a straight line along line \( l \). So ∠1 and ∠2 are a linear pair.

Supplementary angles are two angles whose sum is 180°. A linear pair is supplementary, but also non - adjacent angles can be supplementary. For example, ∠1 and ∠4 are vertical, but ∠1 and ∠3 are supplementary? Wait, no. Let's take ∠1 and ∠2 (linear pair, so supplementary) or ∠1 and ∠4? No, ∠1 and ∠2: they form a linear pair, so sum to 180°, so they are supplementary. Also, ∠3 and ∠5: if lines \( l \) and \( m \) are parallel, but even without, ∠3 and ∠5 could be supplementary? Wait, better to take a linear pair as supplementary. So ∠1 and ∠2 are supplementary.

Answer:

∠1 and ∠4 (or other valid pairs like ∠2 and ∠3, ∠5 and ∠8, ∠6 and ∠7)

(ii) Linear Pair