Question

1. and ∠5 are corresponding angles.
2. ∠7 and angles.
3. ∠8 and are corresponding angles.
4. and angles.
5. and ∠6 are alternate interior angles.
6. ∠3 and angles.
7. ∠2 and are alternate exterior angles.
8. and angles.

identify the pair of congruent angles in each diagram.

1. ≅ ∠3
2. ≅

Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position. Alternate - interior angles are between the two parallel lines and on opposite sides of the transversal. Alternate - exterior angles are outside the two parallel lines and on opposite sides of the transversal. Vertical angles and corresponding angles formed by parallel lines and a transversal are congruent.

Step2: Identify corresponding angles

For the first part (finding corresponding angles):

• If we assume a set of parallel lines cut by a transversal, an angle corresponding to ∠5 would be an angle in the same relative position. Let's assume the standard parallel - line and transversal setup. If ∠5 is given, its corresponding angle is ∠1. Similarly, if we consider ∠8, its corresponding angle is ∠4.

Step3: Identify alternate - interior angles

For alternate - interior angles, if we have ∠6, its alternate - interior angle is ∠3.

Step4: Identify alternate - exterior angles

For alternate - exterior angles, if we have ∠2, its alternate - exterior angle is ∠7.

Step5: Identify congruent angles

In the given diagrams of parallel lines cut by a transversal:

• In the first diagram, ∠1≅∠3 (corresponding angles) and ∠2≅∠3 (alternate - interior angles). In the second diagram, ∠4≅∠6 (alternate - interior angles).

1. ∠1
2. ∠4
3. ∠1
4. (No information for this number in the steps above, assuming it's a repeat or mis - numbered part)
5. ∠3
6. (No information for this number in the steps above, assuming it's a repeat or mis - numbered part)
7. ∠7
8. (No information for this number in the steps above, assuming it's a repeat or mis - numbered part)
9. ∠1
10. ∠4≅∠6

Answer:

1. ∠1
2. ∠4
3. ∠1

4.

1. ∠3

6.

1. ∠7

8.

1. ∠1
2. ∠4≅∠6