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: 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

Looking at the figure, \(\angle1\) and \(\angle2\) are adjacent and form a straight line.

Step3: Identify vertical angles

\(\angle1\) and \(\angle6\) are opposite angles formed by the intersection of lines \(l\) and \(n\).

Step4: Identify congruent angles

Vertical angles are congruent. So \(\angle1\) and \(\angle6\) (from step3) are congruent.

Answer:

(a) \(\angle1\) and \(\angle2\)
(b) \(\angle1\) and \(\angle6\)
(c) \(\angle1\) and \(\angle6\)