Question

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

Explanation:

Step1: Recall Alternate Interior Angles

Alternate interior angles are non - adjacent interior angles on opposite sides of the transversal. For lines \(a\) and \(b\) cut by transversal \(n\), the interior angles are \(\angle3,\angle4,\angle5,\angle6\). A pair of alternate interior angles can be \(\angle3\) and \(\angle6\) (or \(\angle4\) and \(\angle5\)).

Step2: Recall Corresponding Angles

Corresponding angles are in the same position relative to the parallel lines and the transversal. For example, \(\angle1\) and \(\angle5\) (or \(\angle2\) and \(\angle6\), \(\angle3\) and \(\angle7\), \(\angle4\) and \(\angle8\)) are corresponding angles.

Step3: Recall Alternate Exterior Angles

Alternate exterior angles are non - adjacent exterior angles on opposite sides of the transversal. The exterior angles are \(\angle1,\angle2,\angle7,\angle8\). A pair of alternate exterior angles can be \(\angle1\) and \(\angle8\) (or \(\angle2\) and \(\angle7\)).

Answer:

(a) Alternate interior angles: \(\angle3\) and \(\angle6\) (or \(\angle4\) and \(\angle5\))
(b) Corresponding angles: \(\angle1\) and \(\angle5\) (or other valid corresponding angle pairs like \(\angle2\) and \(\angle6\), \(\angle3\) and \(\angle7\), \(\angle4\) and \(\angle8\))
(c) Alternate exterior angles: \(\angle1\) and \(\angle8\) (or \(\angle2\) and \(\angle7\))

(Note: There are multiple correct answers for each part. The above are just examples of valid pairs.)