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: ∠□ and ∠□ (b) vertical angles: ∠□ and ∠□ (c) supplementary angles: ∠□ and ∠□

Explanation:

Part (a)

Step1: Recall linear pair definition

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

Step2: Identify adjacent angles on a line

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

Part (b)

Step1: Recall vertical angles definition

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

Step2: Identify opposite angles

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

Part (c)

Step1: Recall supplementary angles definition

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

Step2: Identify supplementary angles

Using the linear pair from part (a), \(\angle 2\) and \(\angle 3\) are supplementary (since they form a linear pair). (Other valid pairs: any linear pair, or non - adjacent like \(\angle 2\) and \(\angle 4\) are not supplementary, but \(\angle 3\) and \(\angle 6\) (if lines are set such that their sum is \(180^\circ\)), etc.)

Answer:

s:
(a) Linear pair: \(\boldsymbol{\angle 2}\) and \(\boldsymbol{\angle 3}\) (or other valid pair like \(\angle 3\) & \(\angle 4\), etc.)
(b) Vertical angles: \(\boldsymbol{\angle 2}\) and \(\boldsymbol{\angle 4}\) (or other valid pair like \(\angle 3\) & \(\angle 1\), etc.)
(c) Supplementary angles: \(\boldsymbol{\angle 2}\) and \(\boldsymbol{\angle 3}\) (or other valid pair like \(\angle 5\) & \(\angle 6\), etc.)