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:

Step1: Linear Pair Definition

A linear pair of angles are adjacent and form a straight line (sum to \(180^\circ\)). For example, \(\angle 1\) and \(\angle 2\) are adjacent and on a straight line (vertical line \(l\) and horizontal line \(n\)).

Step2: Vertical Angles Definition

Vertical angles are opposite angles formed by intersecting lines, equal in measure. \(\angle 1\) and \(\angle 4\) (or \(\angle 2\) and \(\angle 3\), \(\angle 5\) and \(\angle 8\), \(\angle 6\) and \(\angle 7\)) are vertical.

Step3: Supplementary Angles Definition

Supplementary angles sum to \(180^\circ\). Linear pairs are supplementary, so \(\angle 1\) and \(\angle 2\) (or any linear pair, or non - adjacent like \(\angle 4\) and \(\angle 6\) as they are on a straight line \(n\) with line \(l\) and \(m\) intersecting) are supplementary.

Answer:

s:
(a) \(\angle 1\) and \(\angle 2\) (other valid pairs: \(\angle 2\) and \(\angle 4\), \(\angle 4\) and \(\angle 3\), \(\angle 3\) and \(\angle 1\), \(\angle 5\) and \(\angle 6\), \(\angle 6\) and \(\angle 8\), \(\angle 8\) and \(\angle 7\), \(\angle 7\) and \(\angle 5\))
(b) \(\angle 1\) and \(\angle 4\) (other valid pairs: \(\angle 2\) and \(\angle 3\), \(\angle 5\) and \(\angle 8\), \(\angle 6\) and \(\angle 7\))
(c) \(\angle 1\) and \(\angle 2\) (other valid pairs: any linear pair, or \(\angle 4\) and \(\angle 6\), etc.)

(Note: For each part, multiple correct answers exist. The above are examples. For (a), using \(\angle 1\) and \(\angle 2\); for (b), \(\angle 1\) and \(\angle 4\); for (c), \(\angle 1\) and \(\angle 2\) as a sample response.)

(a) \(\boldsymbol{\angle 1}\) and \(\boldsymbol{\angle 2}\)
(b) \(\boldsymbol{\angle 1}\) and \(\boldsymbol{\angle 4}\)
(c) \(\boldsymbol{\angle 1}\) and \(\boldsymbol{\angle 2}\)