Question

give a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles.
(a) alternate interior angles: \\(\angle \square\\) and \\(\angle \square\\)
(b) corresponding angles: \\(\angle \square\\) and \\(\angle \square\\)
(c) alternate exterior angles: \\(\angle \square\\) and \\(\angle \square\\)

Explanation:

Step1: Recall Angle Definitions

• Alternate Interior Angles: Angles between two lines, on opposite sides of a transversal. For lines \( m, n \) and transversal \( a \), interior angles are \( \angle 3, \angle 4, \angle 5, \angle 6 \). Alternate interior: \( \angle 3 \) and \( \angle 5 \) (or \( \angle 4 \) and \( \angle 6 \)).
• Corresponding Angles: Angles in same position relative to lines and transversal. E.g., \( \angle 1 \) and \( \angle 5 \), \( \angle 2 \) and \( \angle 6 \), \( \angle 3 \) and \( \angle 7 \), \( \angle 4 \) and \( \angle 8 \).
• Alternate Exterior Angles: Angles outside two lines, opposite sides of transversal. Exterior angles: \( \angle 1, \angle 2, \angle 7, \angle 8 \). Alternate exterior: \( \angle 1 \) and \( \angle 7 \) (or \( \angle 2 \) and \( \angle 8 \)).

Step2: Identify Each Pair

(a) Alternate Interior: Choose \( \angle 3 \) and \( \angle 5 \) (or \( \angle 4 \) & \( \angle 6 \)).
(b) Corresponding: Choose \( \angle 1 \) and \( \angle 5 \) (or others as above).
(c) Alternate Exterior: Choose \( \angle 1 \) and \( \angle 7 \) (or \( \angle 2 \) & \( \angle 8 \)).

Answer:

(a) Alternate Interior angles: \( \angle 3 \) and \( \angle 5 \) (or \( \angle 4 \) and \( \angle 6 \))
(b) Corresponding angles: \( \angle 1 \) and \( \angle 5 \) (or \( \angle 2 \) and \( \angle 6 \), \( \angle 3 \) and \( \angle 7 \), \( \angle 4 \) and \( \angle 8 \))
(c) Alternate exterior angles: \( \angle 1 \) and \( \angle 7 \) (or \( \angle 2 \) and \( \angle 8 \))

(Example filled:
(a) \( \angle 3 \) and \( \angle 5 \)
(b) \( \angle 1 \) and \( \angle 5 \)
(c) \( \angle 1 \) and \( \angle 7 \))