Question

1. what are the pairs of alternate interior angles?

a. \\( \angle 3 \\) and \\( \angle 4 ; \angle 5 \\) and \\( \angle 6 \\)
b. \\( \angle 3 \\) and \\( \angle 6 ; \angle 4 \\) and \\( \angle 5 \\)
c. \\( \angle 4 \\) and \\( \angle 6 ; \angle 3 \\) and \\( \angle 5 \\)
d. \\( \angle 5 \\) and \\( \angle 8 ; \angle 6 \\) and \\( \angle 7 \\)

1. which best describes \\( \angle 3 \\) and \\( \angle 7 \\)?

a. alternate exterior angles
b. corresponding angles
c. same - side interior angles
d. supplementary angles

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are non - adjacent interior angles that lie on opposite sides of the transversal.

Step2: Analyze each option for question 1

• Option A: \(∠3\) and \(∠4\) are adjacent, \(∠5\) and \(∠6\) are adjacent. So, this option is wrong.
• Option B: \(∠3\) and \(∠6\) are non - adjacent interior angles on opposite sides of the transversal, \(∠4\) and \(∠5\) are non - adjacent interior angles on opposite sides of the transversal.
• Option C: \(∠4\) and \(∠6\) are same - side interior angles. So, this option is wrong.
• Option D: \(∠5\) and \(∠8\) are adjacent, \(∠6\) and \(∠7\) are adjacent. So, this option is wrong.

Step3: Recall the definition of corresponding angles

Corresponding angles are in the same relative position with respect to the parallel lines and the transversal.

Step4: Analyze question 2

• \(∠3\) and \(∠7\) are in the same relative position with respect to the parallel lines and the transversal.

Answer:

1. B. \(∠3\) and \(∠6\); \(∠4\) and \(∠5\)
2. B. corresponding angles