Question

give a pair of corresponding angles, a pair of alternate exterior angles, and a pair of alternate interior angles.
(a) corresponding angles: ∠□ and ∠□
(b) alternate exterior angles: ∠□ and ∠□
(c) alternate interior angles: ∠□ and ∠□

Explanation:

Step1: Recall Angle Definitions

• Corresponding angles: Angles in the same relative position at each intersection where a transversal crosses two lines. For lines \( m \), \( n \) (parallel, assumed) and transversal \( a \), e.g., \( \angle 5 \) and \( \angle 7 \) (same position: top - left of each intersection).
• Alternate exterior angles: Angles outside the two lines, on opposite sides of the transversal. E.g., \( \angle 5 \) and \( \angle 4 \) ( \( \angle 5 \) is outside \( m,n \), left of transversal; \( \angle 4 \) is outside, right of transversal).
• Alternate interior angles: Angles between the two lines, on opposite sides of the transversal. E.g., \( \angle 2 \) and \( \angle 7 \) (between \( m,n \), \( \angle 2 \) right of transversal, \( \angle 7 \) left of transversal).

Step2: Identify Each Pair

• (a) Corresponding angles: \( \angle 5 \) and \( \angle 7 \) (or other valid pairs like \( \angle 6 \) & \( \angle 8 \), \( \angle 1 \) & \( \angle 3 \), \( \angle 2 \) & \( \angle 4 \)).
• (b) Alternate exterior angles: \( \angle 5 \) and \( \angle 4 \) (or \( \angle 1 \) and \( \angle 8 \)).
• (c) Alternate interior angles: \( \angle 2 \) and \( \angle 7 \) (or \( \angle 6 \) and \( \angle 3 \)).

Answer:

(a) Corresponding angles: \( \boldsymbol{\angle 5} \) and \( \boldsymbol{\angle 7} \) (other valid pairs: \( \angle 6 \) & \( \angle 8 \), \( \angle 1 \) & \( \angle 3 \), \( \angle 2 \) & \( \angle 4 \))
(b) Alternate exterior angles: \( \boldsymbol{\angle 5} \) and \( \boldsymbol{\angle 4} \) (other valid pair: \( \angle 1 \) & \( \angle 8 \))
(c) Alternate interior angles: \( \boldsymbol{\angle 2} \) and \( \boldsymbol{\angle 7} \) (other valid pair: \( \angle 6 \) & \( \angle 3 \))

(Note: Answers may vary as long as they follow the angle definitions. For example, (a) could also be \( \angle 6 \) and \( \angle 8 \), (b) \( \angle 1 \) and \( \angle 8 \), (c) \( \angle 6 \) and \( \angle 3 \).)