Question

for the figure below, give the following.
(a) one pair of vertical angles
(b) one pair of angles that form a linear pair
(c) one pair of angles that are congruent

(a) vertical angles: ∠□ and ∠□
(b) linear pair: ∠□ and ∠□
(c) congruent angles: ∠□ and ∠□
explanation

Explanation:

Part (a) - Vertical Angles

Vertical angles are formed by two intersecting lines and are opposite each other. For example, when line \( l \) intersects line \( n \), \( \angle 1 \) and \( \angle 6 \) are vertical angles (or \( \angle 2 \) and \( \angle 5 \), \( \angle 3 \) and \( \angle 8 \), \( \angle 4 \) and \( \angle 7 \)). Let's take \( \angle 1 \) and \( \angle 6 \).

Part (b) - Linear Pair

A linear pair of angles are adjacent and form a straight line (sum to \( 180^\circ \)). For example, \( \angle 1 \) and \( \angle 2 \) are adjacent and form a straight line (since line \( l \) is straight), so they are a linear pair (or \( \angle 5 \) and \( \angle 6 \), \( \angle 2 \) and \( \angle 3 \), \( \angle 3 \) and \( \angle 4 \), \( \angle 7 \) and \( \angle 8 \), \( \angle 4 \) and \( \angle 8 \), etc.). Let's take \( \angle 1 \) and \( \angle 2 \).

Part (c) - Congruent Angles

Vertical angles are congruent, so we can use the vertical angles from part (a). For example, \( \angle 1 \) and \( \angle 6 \) are congruent (or \( \angle 2 \) and \( \angle 5 \), \( \angle 3 \) and \( \angle 8 \), \( \angle 4 \) and \( \angle 7 \)). Also, if line \( l \) is perpendicular to line \( n \), then \( \angle 1, \angle 2, \angle 5, \angle 6 \) are right angles and congruent. Let's take \( \angle 1 \) and \( \angle 6 \) (or \( \angle 5 \) and \( \angle 2 \) as right angles).

Answer:

s:
(a) Vertical angles: \( \angle 1 \) and \( \angle 6 \) (or other vertical angle pairs like \( \angle 2 \) & \( \angle 5 \), \( \angle 3 \) & \( \angle 8 \), \( \angle 4 \) & \( \angle 7 \))
(b) Linear pair: \( \angle 1 \) and \( \angle 2 \) (or other linear pairs like \( \angle 5 \) & \( \angle 6 \), \( \angle 2 \) & \( \angle 3 \), etc.)
(c) Congruent angles: \( \angle 1 \) and \( \angle 6 \) (or other congruent pairs like vertical angles or right angles if \( l \perp n \))

(Note: Answers may vary slightly based on the exact figure, but the above follows the definitions of vertical angles, linear pairs, and congruent angles.)