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

Explanation:

Step1: Recall definitions

• Linear pair: Two adjacent angles that form a straight line (sum to \(180^{\circ}\)).
• Vertical angles: Opposite angles formed by two intersecting lines.
• Congruent angles: Angles with equal measure.

Step2: Identify linear pair

\(\angle1\) and \(\angle2\) are adjacent and form a straight line (on line \(l\)).

Step3: Identify vertical angles

\(\angle1\) and \(\angle4\) are opposite angles formed by the intersection of lines \(l\) and \(n\).

Step4: Identify congruent angles

Vertical angles are congruent. So \(\angle1\) and \(\angle4\) (also, other vertical - angle pairs like \(\angle2\) and \(\angle3\), \(\angle5\) and \(\angle8\), \(\angle6\) and \(\angle7\) can be considered).

Answer:

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