Question

1. name two pairs of alternate interior angles.
2. what is the relationship between ∠2 and ∠8?
3. which postulate or theorem justifies that ∠3 is supplementary to ∠6?
4. which postulate or theorem justifies that m∠4 is equal to m∠8?

Explanation:

Step1: Recall alternate - interior angles

Alternate - interior angles are formed when a transversal intersects two lines. For example, if we have two parallel lines \(l_1\) and \(l_2\) and a transversal \(t\), the pairs are non - adjacent angles between the two lines and on opposite sides of the transversal.

Step2: Identify pairs for question 1

Let the two parallel lines be \(l_1\) and \(l_2\) and transversal \(t\). One pair could be \(\angle3\) and \(\angle6\), another pair could be \(\angle4\) and \(\angle5\).

Step3: Recall angle relationships for question 2

\(\angle2\) and \(\angle8\) are alternate exterior angles. They are non - adjacent angles outside the two lines and on opposite sides of the transversal.

Step4: Recall supplementary - angle postulates for question 3

\(\angle3\) and \(\angle6\) are same - side interior angles. The Same - Side Interior Angles Postulate states that when two parallel lines are cut by a transversal, same - side interior angles are supplementary.

Step5: Recall equal - angle postulates for question 4

\(\angle4\) and \(\angle8\) are corresponding angles. The Corresponding Angles Postulate states that when two parallel lines are cut by a transversal, corresponding angles are congruent, so \(m\angle4=m\angle8\).

Answer:

1. \(\angle3\) and \(\angle6\), \(\angle4\) and \(\angle5\)
2. Alternate exterior angles
3. Same - Side Interior Angles Postulate
4. Corresponding Angles Postulate