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 congruent
(a) linear pair:
(b) vertical angles:
(c) congruent angles:

Explanation:

Step1: Recall definitions

• A linear pair of angles is a pair of adjacent angles whose non - common sides are opposite rays.
• Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines.
• Congruent angles are angles that have the same measure.

Step2: Find linear pair

For a linear pair, we can consider adjacent angles. For example, \(\angle1\) and \(\angle2\) are adjacent and their non - common sides form a straight line.

Step3: Find vertical angles

Vertical angles are formed by the intersection of two lines. \(\angle1\) and \(\angle4\) are non - adjacent and formed by the intersection of lines \(l\) and \(n\).

Step4: Find congruent angles

Vertical angles are congruent. So, \(\angle1\) and \(\angle4\) (from vertical angles) are congruent. Also, if we assume some parallel line properties (not given in the problem statement but based on general geometric figures), we can have other congruent pairs. But using the vertical - angle property: \(\angle1\cong\angle4\)

Answer:

(a) Linear pair: \(\angle1\) and \(\angle2\)
(b) Vertical angles: \(\angle1\) and \(\angle4\)
(c) Congruent angles: \(\angle1\) and \(\angle4\)