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If two lines are parallel and a transversal creates a pair of interior angles th

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Question: If two lines are parallel and a transversal creates a pair of interior angles that are supplementary, what can be concluded about the lines?

Options:

  1. They are not parallel.
  2. They are perpendicular.
  3. They are parallel.
  4. They intersect.

Correct Answer: They are not parallel.

Solution: 

If the interior angles are supplementary, it indicates that the lines are not parallel, as parallel lines would create equal alternate interior angles.

If two lines are parallel and a transversal creates a pair of interior angles th

Practice Questions

Q1
If two lines are parallel and a transversal creates a pair of interior angles that are supplementary, what can be concluded about the lines?
  1. They are not parallel.
  2. They are perpendicular.
  3. They are parallel.
  4. They intersect.

Questions & Step-by-Step Solutions

If two lines are parallel and a transversal creates a pair of interior angles that are supplementary, what can be concluded about the lines?
  • Step 1: Understand what parallel lines are. Parallel lines are lines that never meet and are always the same distance apart.
  • Step 2: Know what a transversal is. A transversal is a line that crosses two or more other lines.
  • Step 3: Identify what interior angles are. Interior angles are the angles that are formed inside the two lines when a transversal crosses them.
  • Step 4: Learn about supplementary angles. Supplementary angles are two angles that add up to 180 degrees.
  • Step 5: If the interior angles created by the transversal are supplementary, it means they add up to 180 degrees.
  • Step 6: Recall the property of parallel lines. When two lines are parallel, the interior angles formed by a transversal are equal, not supplementary.
  • Step 7: Conclude that if the interior angles are supplementary, the lines cannot be parallel.
  • Parallel Lines and Transversals – When two parallel lines are intersected by a transversal, the interior angles formed are equal and not supplementary.
  • Supplementary Angles – Supplementary angles are two angles that add up to 180 degrees, which indicates that the lines cannot be parallel if the interior angles are supplementary.
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