Question

directions: given the diagram below, determine whether the angle pars are corresponding, alternate interior, alternate exterior, consecutive interior, or no relationship. use the answer bank provided. answer choices: a - corresponding b - alternate int. c - alternate ext. d - consecutive int. e - no relationship 1. b ∠2 and ∠13 2. d ∠4 and ∠11 3. e ∠1 and ∠16 4. b ∠8 and ∠11 5. d ∠3 and ∠5 6. ∠14 and ∠16 7. a ∠1 and ∠3 8. ∠5 and ∠10 9. ∠13 and ∠15 10. e ∠4 and ∠5 11. ∠4 and ∠13 12. ∠2 and ∠7 13. ∠4 and ∠12 14. c ∠3 and ∠16 15. ∠12 and ∠14 16. a ∠7 and ∠15 17. ∠6 and ∠16 18. ∠11 and ∠14 19. ∠1 and ∠3 20. e ∠1 and ∠11

Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position at each intersection where a straight - line crosses two others. Alternate interior angles are between the two lines and on opposite sides of the transversal. Alternate exterior angles are outside the two lines and on opposite sides of the transversal. Consecutive interior angles are between the two lines and on the same side of the transversal.

Step2: Analyze each angle - pair

1. $\angle14$ and $\angle16$ are corresponding angles. (Same relative position at the intersections)
2. $\angle5$ and $\angle10$ have no relationship. (Not in any of the special angle - pair categories)
3. $\angle13$ and $\angle15$ have no relationship. (Not in any of the special angle - pair categories)
4. $\angle4$ and $\angle13$ have no relationship. (Not in any of the special angle - pair categories)
5. $\angle2$ and $\angle7$ are alternate exterior angles. (Outside the two lines and on opposite sides of the transversal)
6. $\angle4$ and $\angle12$ are corresponding angles. (Same relative position at the intersections)
7. $\angle12$ and $\angle14$ have no relationship. (Not in any of the special angle - pair categories)
8. $\angle6$ and $\angle16$ have no relationship. (Not in any of the special angle - pair categories)
9. $\angle11$ and $\angle14$ have no relationship. (Not in any of the special angle - pair categories)
10. $\angle1$ and $\angle3$ are corresponding angles. (Same relative position at the intersections)

Answer:

1. A. Corresponding
2. E. No Relationship
3. E. No Relationship
4. E. No Relationship
5. C. Alternate Ext.
6. A. Corresponding
7. E. No Relationship
8. E. No Relationship
9. E. No Relationship
10. A. Corresponding