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If two parallel lines are cut by a transversal and one of the interior angles is

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Question: If two parallel lines are cut by a transversal and one of the interior angles is 45 degrees, what is the measure of the same-side interior angle?

Options:

  1. 45 degrees
  2. 135 degrees
  3. 90 degrees
  4. 180 degrees

Correct Answer: 135 degrees

Solution: 

Same-side interior angles are supplementary when two parallel lines are cut by a transversal. Therefore, 180 - 45 = 135 degrees.

If two parallel lines are cut by a transversal and one of the interior angles is

Practice Questions

Q1
If two parallel lines are cut by a transversal and one of the interior angles is 45 degrees, what is the measure of the same-side interior angle?
  1. 45 degrees
  2. 135 degrees
  3. 90 degrees
  4. 180 degrees

Questions & Step-by-Step Solutions

If two parallel lines are cut by a transversal and one of the interior angles is 45 degrees, what is the measure of the same-side interior angle?
  • Step 1: Understand that we have two parallel lines and a transversal cutting through them.
  • Step 2: Identify that one of the interior angles formed by the transversal and the parallel lines is 45 degrees.
  • Step 3: Recall that same-side interior angles are supplementary, which means they add up to 180 degrees.
  • Step 4: To find the measure of the same-side interior angle, subtract the known angle from 180 degrees: 180 - 45.
  • Step 5: Calculate the result: 180 - 45 = 135 degrees.
  • Step 6: Conclude that the measure of the same-side interior angle is 135 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 – Two angles are supplementary if the sum of their measures is 180 degrees.
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