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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 75 degrees, what is the measure of the other same-side interior angle?

Options:

  1. 75 degrees
  2. 105 degrees
  3. 90 degrees
  4. 180 degrees

Correct Answer: 105 degrees

Solution: 

Same-side interior angles are supplementary, so the other angle measures 105 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 75 degrees, what is the measure of the other same-side interior angle?
  1. 75 degrees
  2. 105 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 same-side interior angles is 75 degrees, what is the measure of the other same-side interior angle?
  • Step 1: Understand that same-side interior angles are the angles that are on the same side of the transversal and between the two parallel lines.
  • Step 2: Remember that same-side interior angles are supplementary, which means they add up to 180 degrees.
  • Step 3: You are given one angle that measures 75 degrees.
  • Step 4: To find the other angle, subtract the given angle from 180 degrees: 180 - 75.
  • Step 5: Calculate 180 - 75, which equals 105 degrees.
  • Step 6: Therefore, the measure of the other same-side interior angle is 105 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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