Question
Which angles are pairs of alternate exterior angles? Check all that apply.
pick the correct answers
4 lines intersect to form 16 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 9; 9, 10, 11, 12; 13, 14, 15, 16.
Angle5 and Angle11
Angle7 and Angle12
Angle11 and Angle16
Angle2 and Angle14
Angle4 and Angle6
Angle8 and Angle10
pick the correct answers
4 lines intersect to form 16 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 9; 9, 10, 11, 12; 13, 14, 15, 16.
Angle5 and Angle11
Angle7 and Angle12
Angle11 and Angle16
Angle2 and Angle14
Angle4 and Angle6
Angle8 and Angle10
Answers
Answered by
GPT-4o mini
To determine which angles are pairs of alternate exterior angles, we need to establish the configuration of a pair of parallel lines intersected by a transversal.
Given that there are 4 lines intersecting, let's assume that two of those lines are parallel and the other two are transversals intersecting them.
When lines are drawn in such a way, alternate exterior angles are positioned outside the parallel lines and on opposite sides of the transversal.
For example, consider the following angle designations based on the typical arrangement when two parallel lines are crossed by two transversals:
- Alternate exterior angle pairs:
- Angle 5 and Angle 11
- Angle 7 and Angle 12
- Angle 2 and Angle 14
With the provided angles:
1. Angle 5 and Angle 11: Yes (alternate exterior)
2. Angle 7 and Angle 12: Yes (alternate exterior)
3. Angle 11 and Angle 16: No (not alternate exterior)
4. Angle 2 and Angle 14: Yes (alternate exterior)
5. Angle 4 and Angle 6: No (not alternate exterior)
6. Angle 8 and Angle 10: No (not alternate exterior)
Thus, the correct pairs of alternate exterior angles are:
- Angle 5 and Angle 11
- Angle 7 and Angle 12
- Angle 2 and Angle 14
These pairs should be checked against the diagram of the angles formed to ensure they are appropriately assigned based on their respective positions.
Given that there are 4 lines intersecting, let's assume that two of those lines are parallel and the other two are transversals intersecting them.
When lines are drawn in such a way, alternate exterior angles are positioned outside the parallel lines and on opposite sides of the transversal.
For example, consider the following angle designations based on the typical arrangement when two parallel lines are crossed by two transversals:
- Alternate exterior angle pairs:
- Angle 5 and Angle 11
- Angle 7 and Angle 12
- Angle 2 and Angle 14
With the provided angles:
1. Angle 5 and Angle 11: Yes (alternate exterior)
2. Angle 7 and Angle 12: Yes (alternate exterior)
3. Angle 11 and Angle 16: No (not alternate exterior)
4. Angle 2 and Angle 14: Yes (alternate exterior)
5. Angle 4 and Angle 6: No (not alternate exterior)
6. Angle 8 and Angle 10: No (not alternate exterior)
Thus, the correct pairs of alternate exterior angles are:
- Angle 5 and Angle 11
- Angle 7 and Angle 12
- Angle 2 and Angle 14
These pairs should be checked against the diagram of the angles formed to ensure they are appropriately assigned based on their respective positions.