The angle pairs in the diagram are:
1 and 11: Corresponding angles
2 and 11: Alternate interior angles
3 and 5: Consecutive interior angles
4 and 8: Alternate exterior angles
Therefore, the answer is 1, 2, 3, and 4.
To classify the angle pairs in the diagram, we first need to identify the transversal.
The transversal is line PQ.
Corresponding angles are two angles that are in the same position relative to the transversal and on the same side of the transversal.
Corresponding angles are always congruent.
In the diagram, the following angle pairs are corresponding angles:
∠1 and ∠11
∠2 and ∠15
∠3 and ∠16
∠4 and ∠7
∠5 and ∠8
∠6 and ∠9
∠10 and ∠13
∠12 and ∠14
Alternate interior angles are two non-adjacent interior angles on opposite sides of the transversal.
Alternate interior angles are always congruent. In the diagram, the following angle pairs are alternate interior angles:
∠2 and ∠11
∠3 and ∠16
∠5 and ∠8
∠6 and ∠9
Consecutive interior angles are two adjacent interior angles on the same side of the transversal.
Consecutive interior angles are supplementary, meaning that their sum is 180 degrees.
In the diagram, the following angle pairs are consecutive interior angles:
∠3 and ∠5
∠8 and ∠10
Alternate exterior angles are two non-adjacent exterior angles on opposite sides of the transversal.
Alternate exterior angles are always congruent.
In the diagram, the following angle pairs are alternate exterior angles:
∠4 and ∠14
∠7 and ∠13
Therefore, the angle pairs in the diagram can be classified as follows:
Corresponding angles: 1, 2, 3, 4, 5, 6, 10, 12
Alternate interior angles: 2, 3, 5, 6
Consecutive interior angles: 3, 5, 8, 10
Alternate exterior angles: 4, 7