Question

for the figure below, give the following.
(a) one pair of angles that form a linear pair
(b) one pair of vertical angles
(c) one pair of angles that are supplementary

(a) linear pair: \\(\angle \square\\) and \\(\angle \square\\)
(b) vertical angles: \\(\angle \square\\) and \\(\angle \square\\)
(c) supplementary angles: \\(\angle \square\\) and \\(\angle \square\\)

Explanation:

Part (a)

Step 1: Recall Linear Pair Definition

A linear pair of angles are adjacent and form a straight line (sum to \(180^\circ\)).

Step 2: Identify Linear Pair

\(\angle 1\) and \(\angle 2\) are adjacent, share a common side, and their non - common sides form a straight line \(l\). So \(\angle 1\) and \(\angle 2\) form a linear pair. (Other possible pairs: \(\angle 3\) and \(\angle 4\), \(\angle 5\) and \(\angle 6\), \(\angle 7\) and \(\angle 8\), \(\angle 1\) and \(\angle 3\) etc.)

Part (b)

Step 1: Recall Vertical Angles Definition

Vertical angles are opposite angles formed by the intersection of two lines, and they are equal.

Step 2: Identify Vertical Angles

When line \(n\) intersects line \(l\), \(\angle 1\) and \(\angle 4\) are opposite angles. So \(\angle 1\) and \(\angle 4\) are vertical angles. (Other possible pairs: \(\angle 2\) and \(\angle 3\), \(\angle 5\) and \(\angle 8\), \(\angle 6\) and \(\angle 7\))

Part (c)

Step 1: Recall Supplementary Angles Definition

Supplementary angles are two angles whose sum is \(180^\circ\).

Step 2: Identify Supplementary Angles

\(\angle 1\) and \(\angle 2\) (from linear pair, sum to \(180^\circ\)) are supplementary. (Other possible pairs: \(\angle 3\) and \(\angle 4\), \(\angle 1\) and \(\angle 3\), \(\angle 5\) and \(\angle 6\) etc.)

Answer:

s:
(a) \(\angle 1\) and \(\angle 2\) (or other valid linear pair)
(b) \(\angle 1\) and \(\angle 4\) (or other valid vertical pair)
(c) \(\angle 1\) and \(\angle 2\) (or other valid supplementary pair)

(Note: For (a), (b), (c) there are multiple correct answers. The above are examples. For instance, in (a) \(\angle 3\) and \(\angle 4\) is also correct; in (b) \(\angle 2\) and \(\angle 3\) is correct; in (c) \(\angle 3\) and \(\angle 4\) is correct.)