Question

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

Explanation:

Step1: Recall Angle Definitions

• Alternate interior angles: Lie between two lines, on opposite sides of a transversal.
• Alternate exterior angles: Lie outside two lines, on opposite sides of a transversal.
• Corresponding angles: Occupy the same relative position at each intersection.

Step2: Identify Alternate Interior Angles

For lines \( g \), \( h \), transversal \( m \), interior angles between \( g \), \( h \) are \( \angle 3, \angle 5 \) (or \( \angle 4, \angle 6 \)). Let's take \( \angle 3 \) and \( \angle 5 \).

Step3: Identify Alternate Exterior Angles

Exterior angles outside \( g \), \( h \) are \( \angle 2 \) and \( \angle 8 \) (or \( \angle 1 \) and \( \angle 7 \)). Let's take \( \angle 2 \) and \( \angle 8 \).

Step4: Identify Corresponding Angles

Corresponding angles: \( \angle 2 \) and \( \angle 6 \) (or \( \angle 3 \) and \( \angle 7 \), \( \angle 1 \) and \( \angle 5 \), \( \angle 4 \) and \( \angle 8 \)). Let's take \( \angle 2 \) and \( \angle 6 \).

Answer:

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

(Note: Answers may vary as long as they follow the angle relationship definitions.)