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If two parallel lines are cut by a transversal and the sum of the interior angle

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Question: If two parallel lines are cut by a transversal and the sum of the interior angles on the same side of the transversal is 180 degrees, what can be concluded?

Options:

  1. The lines are not parallel.
  2. The lines are perpendicular.
  3. The angles are equal.
  4. The angles are supplementary.

Correct Answer: The angles are supplementary.

Solution: 

Interior angles on the same side of the transversal are supplementary when two parallel lines are cut by a transversal.

If two parallel lines are cut by a transversal and the sum of the interior angle

Practice Questions

Q1
If two parallel lines are cut by a transversal and the sum of the interior angles on the same side of the transversal is 180 degrees, what can be concluded?
  1. The lines are not parallel.
  2. The lines are perpendicular.
  3. The angles are equal.
  4. The angles are supplementary.

Questions & Step-by-Step Solutions

If two parallel lines are cut by a transversal and the sum of the interior angles on the same side of the transversal is 180 degrees, what can be concluded?
  • Step 1: Identify the two parallel lines and the transversal that cuts across them.
  • Step 2: Observe the angles formed on the same side of the transversal.
  • Step 3: Measure the sum of these two interior angles.
  • Step 4: If the sum of these angles equals 180 degrees, this means they are supplementary.
  • Step 5: Conclude that when two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are always supplementary.
  • Supplementary Angles – When two angles add up to 180 degrees, they are considered supplementary.
  • Transversal and Parallel Lines – A transversal is a line that intersects two or more lines, and when it intersects parallel lines, specific angle relationships are established.
  • Interior Angles – Interior angles are the angles formed on the inside of the parallel lines when cut by a transversal.
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