Question

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

Explanation:

Step1: Identify Alternate Exterior Angles

Alternate exterior angles are outside the two lines and on opposite sides of the transversal. Here, ∠2 and ∠7 (or ∠1 and ∠6) are alternate exterior. Let's take ∠2 and ∠7.

Step2: Identify Corresponding Angles

Corresponding angles are in the same position relative to the lines and transversal. ∠3 and ∠7 (or ∠2 and ∠6, ∠1 and ∠5, ∠4 and ∠8) are corresponding. Let's take ∠3 and ∠7.

Step3: Identify Alternate Interior Angles

Alternate interior angles are between the two lines and on opposite sides of the transversal. ∠3 and ∠5 (or ∠4 and ∠6) are alternate interior. Let's take ∠3 and ∠5.

Answer:

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

(Note: Other valid pairs exist based on angle position definitions. The above are common correct examples.)