Question

classify each angle pair or write “none”: 1. <9 and <11 2. <9 and <1 3. <11 and <4 4. <9 and <4 5. <10 and <1 6. <3 and <12 7. <12 and <1

Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position with respect to the transversal and the parallel lines. Vertical angles are opposite each other when two lines intersect. Same - side interior angles are on the same side of the transversal and inside the two lines. Same - side exterior angles are on the same side of the transversal and outside the two lines. Alternate exterior angles are on opposite sides of the transversal and outside the two lines. Alternate interior angles are on opposite sides of the transversal and inside the two lines. Linear pairs are adjacent and supplementary.

Step2: Analyze ∠9 and ∠11

They are vertical angles (VA) since they are opposite each other where two lines intersect.

Step3: Analyze ∠9 and ∠1

They are alternate exterior angles (AEA) as they are on opposite sides of the transversal and outside the two lines.

Step4: Analyze ∠11 and ∠4

They are alternate interior angles (AIA) as they are on opposite sides of the transversal and inside the two lines.

Step5: Analyze ∠9 and ∠4

None (NA) as they do not fit any of the standard angle - pair relationships.

Step6: Analyze ∠10 and ∠1

They are corresponding angles (CA) as they are in the same relative position with respect to the transversal and the two lines.

Step7: Analyze ∠3 and ∠12

They are alternate exterior angles (AEA) as they are on opposite sides of the transversal and outside the two lines.

Step8: Analyze ∠12 and ∠1

None (NA) as they do not fit any of the standard angle - pair relationships.

Answer:

1. VA
2. AEA
3. AIA
4. NA
5. CA
6. AEA
7. NA