Question

test - transversals - a name_ class _ a. corresponding b. same side interior c. alternate interior d. vertical angles e. same side exterior f. alternate exterior g. linear pair h. no relationship identify each type of angle pair from the given figure. 1. ∠1 and ∠7 _ 2. ∠1 and ∠11 _ 3. ∠6 and ∠9 _ 4. ∠4 and ∠5 _ 5. ∠2 and ∠10 _ 6. ∠2 and ∠3 _ 7. ∠3 and ∠7 _ 8. ∠4 and ∠7 _ 9. ∠12 and ∠6 _ 10. ∠1 and ∠9 _ 11. ∠8 and ∠10 _ 12. ∠8 and ∠4 _ in the figure given, a || b. find the measures of each indicated angle. 13. m∠1 = _ 14. m∠2 = _ 15. m∠3 = _ 16. m∠4 = _ 17. m∠5 = _ 18. m∠6 = _

Explanation:

Step1: Identify angle pairs

• ∠1 and ∠7: Alternate exterior angles (F).
• ∠1 and ∠11: Alternate exterior angles (F).
• ∠6 and ∠9: Vertical angles (D).
• ∠4 and ∠5: Linear pair (G).
• ∠2 and ∠10: Corresponding angles (A).
• ∠2 and ∠3: Linear pair (G).
• ∠3 and ∠7: Corresponding angles (A).
• ∠4 and ∠7: No relationship (H).
• ∠12 and ∠6: Alternate interior angles (C).
• ∠1 and ∠9: No relationship (H).
• ∠8 and ∠10: Same - side interior angles (B).
• ∠8 and ∠4: Alternate interior angles (C).

Step2: Find angle measures

• Given \(a\parallel b\) and one angle is \(96^{\circ}\).
• \(m\angle1 = 96^{\circ}\) (vertical angles).
• \(m\angle2=180 - 96=84^{\circ}\) (linear pair).
• \(m\angle3 = 84^{\circ}\) (vertical angles).
• \(m\angle4 = 96^{\circ}\) (corresponding angles to \(\angle1\)).
• \(m\angle5 = 84^{\circ}\) (vertical angles to \(\angle3\)).
• \(m\angle6 = 96^{\circ}\) (vertical angles to \(\angle4\)).

Answer:

1. F
2. F
3. D
4. G
5. A
6. G
7. A
8. H
9. C
10. H
11. B
12. C
13. \(96^{\circ}\)
14. \(84^{\circ}\)
15. \(84^{\circ}\)
16. \(96^{\circ}\)
17. \(84^{\circ}\)
18. \(96^{\circ}\)