Answer:
Not parallel.
Step-by-step explanation:
Given:
Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
Angles 9 and 10 form a linear pair:
⇒ m∠9 + m∠10 = 180°
⇒ 110° + m∠10 = 180°
⇒ m∠10 = 70°
Angles 7 and 8 form a linear pair:
⇒ m∠7 + m∠8 = 180°
⇒ m∠7 + 70° = 180°
⇒ m∠7 = 110°
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
As line p is parallel to line q, and according to the vertical angles theorem and the corresponding angles postulate:
- m∠1 = m∠6 = m∠9 = m∠14 = 110°
- m∠2 = m∠5 = m∠10 = m∠13 = 70°
- m∠3 = m∠8 = m∠11 = m∠16 = 70°
- m∠4 = m∠7 = m∠12 = m∠15 = 110°
If line a was parallel to line b, then according to the corresponding angles postulate:
- m∠1 = m∠3 = m∠6 = m∠8
- m∠2 = m∠4 = m∠5 = m∠7
As m∠1 ≠ m∠8 and m∠2 ≠ m∠7 then lines a and b are not parallel.
