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)

Step1: Recall linear pair definition

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

Step2: Identify adjacent angles on a line

\(\angle 1\) and \(\angle 2\) are adjacent, share a side, and form a straight line (along line \(l\)).

Part (b)

Step1: Recall vertical angles definition

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

Step2: Identify opposite angles

\(\angle 5\) and \(\angle 2\) (or \(\angle 6\) and \(\angle 1\), \(\angle 7\) and \(\angle 4\), \(\angle 8\) and \(\angle 3\)) are vertical. Here, \(\angle 5\) and \(\angle 2\) (or another valid pair like \(\angle 6\) and \(\angle 1\)).

Part (c)

Step1: Recall supplementary angles definition

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

Step2: Identify supplementary pair

\(\angle 3\) and \(\angle 8\) (or \(\angle 3\) and \(\angle 7\), \(\angle 4\) and \(\angle 8\), \(\angle 4\) and \(\angle 7\), or linear pair like \(\angle 1\) and \(\angle 2\)). Here, \(\angle 3\) and \(\angle 8\) (or another valid pair).

Answer:

s:
(a) Linear pair: \(\angle 1\) and \(\angle 2\) (other valid pairs: \(\angle 5\) and \(\angle 6\), \(\angle 3\) and \(\angle 4\), \(\angle 7\) and \(\angle 8\), \(\angle 2\) and \(\angle 6\), etc.)
(b) Vertical angles: \(\angle 5\) and \(\angle 2\) (other valid pairs: \(\angle 6\) and \(\angle 1\), \(\angle 7\) and \(\angle 4\), \(\angle 8\) and \(\angle 3\))
(c) Supplementary angles: \(\angle 3\) and \(\angle 8\) (other valid pairs: \(\angle 3\) and \(\angle 7\), \(\angle 4\) and \(\angle 8\), \(\angle 4\) and \(\angle 7\), \(\angle 1\) and \(\angle 2\), etc.)

(Note: For each part, any valid pair following the angle relationship definitions is acceptable.)