Question

(a) linear pair: ∠ and ∠ (b) vertical angles: ∠ and ∠ (c) supplementary angles: ∠ and ∠

Explanation:

Step1: Identify linear pair

A linear pair of angles is adjacent and supplementary (sum to \(180^{\circ}\)). For example, \(\angle1\) and \(\angle2\) (they are adjacent and form a straight - line along the transversal \(n\) intersected by line \(l\)).

Step2: Identify vertical angles

Vertical angles are opposite angles formed by two intersecting lines. For example, \(\angle1\) and \(\angle3\) (formed by the intersection of line \(l\) and transversal \(n\)).

Step3: Identify supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\). For example, \(\angle1\) and \(\angle4\) (they can be adjacent or non - adjacent, here they are adjacent and form a linear pair, but the concept of supplementary is more general. Another example could be \(\angle5\) and \(\angle7\) if we consider other relationships, but for simplicity, using the basic ones from the figure).

Answer:

(a) Linear pair: \(\angle1\) and \(\angle2\) (answers may vary depending on the pair chosen from the figure, another valid pair could be \(\angle5\) and \(\angle6\) etc.)
(b) Vertical angles: \(\angle1\) and \(\angle3\) (another valid pair could be \(\angle6\) and \(\angle7\) etc.)
(c) Supplementary angles: \(\angle1\) and \(\angle4\) (another valid pair could be \(\angle2\) and \(\angle4\) etc.)