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If two parallel lines are cut by a transversal and one of the same-side interior

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Question: If two parallel lines are cut by a transversal and one of the same-side interior angles is 40 degrees, what is the measure of the other same-side interior angle?

Options:

  1. 40 degrees
  2. 140 degrees
  3. 180 degrees
  4. 90 degrees

Correct Answer: 140 degrees

Solution: 

Same-side interior angles are supplementary when two parallel lines are cut by a transversal. Therefore, the other angle measures 180 - 40 = 140 degrees.

If two parallel lines are cut by a transversal and one of the same-side interior

Practice Questions

Q1
If two parallel lines are cut by a transversal and one of the same-side interior angles is 40 degrees, what is the measure of the other same-side interior angle?
  1. 40 degrees
  2. 140 degrees
  3. 180 degrees
  4. 90 degrees

Questions & Step-by-Step Solutions

If two parallel lines are cut by a transversal and one of the same-side interior angles is 40 degrees, what is the measure of the other same-side interior angle?
  • Step 1: Understand that we have two parallel lines and a transversal cutting through them.
  • Step 2: Identify the same-side interior angles formed by the transversal and the parallel lines.
  • Step 3: Recall that same-side interior angles are supplementary, which means they add up to 180 degrees.
  • Step 4: Since one of the same-side interior angles is given as 40 degrees, we can find the other angle.
  • Step 5: Use the formula for supplementary angles: 180 degrees - 40 degrees.
  • Step 6: Calculate the other angle: 180 - 40 = 140 degrees.
  • Step 7: Conclude that the measure of the other same-side interior angle is 140 degrees.
  • Same-side interior angles – When two parallel lines are cut by a transversal, the same-side interior angles are supplementary, meaning they add up to 180 degrees.
  • Transversal – A transversal is a line that intersects two or more lines at distinct points, creating various angle relationships.
  • Supplementary angles – Supplementary angles are two angles whose measures add up to 180 degrees.
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