Question

Is a || b? Explain using angle measurements. Your response should contain at least 3 full sentences describing how you determined the answer to this question. Angle measurements should be included as part of your explanation. NO PLAGIARISM!

Answer 1

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Answer:

  no

Step-by-step explanation:

Angles 6 and 9 are alternate interior angles where transversal 'a' crosses parallel lines p and q. As such, they are congruent. This means the measure of angle 6 is the same as that of angle 9, 110°.

Angles 6 and 8 are corresponding angles. If lines 'a' and 'b' were parallel, those angles would be congruent. We know angle 6 has a measure of 110° and angle 8 has a measure of 70°, so the angles are not congruent. Hence, lines 'a' and 'b' are not parallel.

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Alternate solutions

Since you are not allowed to plagiarize my answer, you may be interested in other ways to show the same thing. The basic idea is to use angle relationships where transversals cross parallel lines. Ones that can be useful here are ...

• corresponding angles are congruent
• vertical angles are congruent*
• alternate interior (or exterior) angles are congruent
• sequential interior (or exterior) angles are supplementary.
• angles of a linear pair are supplementary*

The relations marked with an asterisk (*) apply where any lines cross, and have no specific relationship to parallel lines. The remaining relationships only occur if the lines are parallel. Showing one of those is not true will show that the lines are not parallel.