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In a transversal intersecting two parallel lines, if one of the interior angles

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Question: In a transversal intersecting two parallel lines, if one of the interior angles measures 75 degrees, what is the measure of the adjacent interior angle?

Options:

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

Correct Answer: 105 degrees

Solution: 

Adjacent interior angles are supplementary, so the adjacent angle = 180 - 75 = 105 degrees.

In a transversal intersecting two parallel lines, if one of the interior angles

Practice Questions

Q1
In a transversal intersecting two parallel lines, if one of the interior angles measures 75 degrees, what is the measure of the adjacent interior angle?
  1. 75 degrees
  2. 105 degrees
  3. 180 degrees
  4. 90 degrees

Questions & Step-by-Step Solutions

In a transversal intersecting two parallel lines, if one of the interior angles measures 75 degrees, what is the measure of the adjacent interior angle?
  • Step 1: Understand that a transversal is a line that crosses two parallel lines.
  • Step 2: Identify that when a transversal intersects parallel lines, it creates pairs of interior angles.
  • Step 3: Recognize that adjacent interior angles (angles next to each other) are supplementary, meaning they add up to 180 degrees.
  • Step 4: If one of the interior angles measures 75 degrees, write down this measurement.
  • Step 5: To find the measure of the adjacent interior angle, subtract the known angle from 180 degrees: 180 - 75.
  • Step 6: Calculate the result: 180 - 75 = 105 degrees.
  • Step 7: Conclude that the measure of the adjacent interior angle is 105 degrees.
  • Transversal and Parallel Lines – Understanding the relationship between angles formed when a transversal intersects parallel lines, specifically that adjacent interior angles are supplementary.
  • Supplementary Angles – Recognizing that two angles are supplementary if their measures add up to 180 degrees.
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