Question

is a parallel to b? Explain using angels and measurements. Angel measrment should be part of your explanation.​

Answer 1

Not parallel.

Explanation:

Given:

• m∠9 = 110°
• m∠8 = 70°

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.