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

Explanation:

Part (a) - Linear Pair

Step1: Recall Linear Pair Definition

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

Step2: Identify Adjacent Angles on a Line

Angles \(\angle 1\) and \(\angle 2\) are adjacent and form a straight line (they lie on line \(l\) and \(n\) intersection). So \(\angle 1\) and \(\angle 2\) form a linear pair. (Other valid pairs: \(\angle 2\) & \(\angle 4\), \(\angle 4\) & \(\angle 3\), \(\angle 3\) & \(\angle 1\), \(\angle 5\) & \(\angle 6\), \(\angle 6\) & \(\angle 8\), \(\angle 8\) & \(\angle 7\), \(\angle 7\) & \(\angle 5\))

Step1: Recall Vertical Angles Definition

Vertical angles are opposite angles formed by intersecting lines (equal in measure).

Step2: Identify Opposite Angles

When lines \(l\) and \(n\) intersect, \(\angle 1\) and \(\angle 4\) are opposite. (Other valid pairs: \(\angle 2\) & \(\angle 3\), \(\angle 5\) & \(\angle 8\), \(\angle 6\) & \(\angle 7\))

Step1: Recall Supplementary Angles Definition

Supplementary angles sum to \(180^\circ\) (can be adjacent or non - adjacent).

Step2: Identify Supplementary Angles

\(\angle 1\) and \(\angle 5\) are supplementary? No, better: \(\angle 1\) and \(\angle 2\) (linear pair, so supplementary). Or \(\angle 1\) and \(\angle 4\) are vertical, but \(\angle 1\) and \(\angle 3\) (linear pair). Also, \(\angle 5\) and \(\angle 6\) (linear pair, supplementary). Let's take \(\angle 1\) and \(\angle 2\) (they sum to \(180^\circ\)).

Answer:

(a): \(\angle 1\) and \(\angle 2\) (or other valid linear pair)

Part (b) - Vertical Angles