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If two lines are parallel and the transversal creates an angle of 30 degrees wit

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Question: If two lines are parallel and the transversal creates an angle of 30 degrees with one of the lines, what is the measure of the same-side interior angle?

Options:

  1. 30 degrees
  2. 150 degrees
  3. 180 degrees
  4. 120 degrees

Correct Answer: 120 degrees

Solution: 

Same-side interior angles are supplementary, so the same-side interior angle is 180 - 30 = 150 degrees.

If two lines are parallel and the transversal creates an angle of 30 degrees wit

Practice Questions

Q1
If two lines are parallel and the transversal creates an angle of 30 degrees with one of the lines, what is the measure of the same-side interior angle?
  1. 30 degrees
  2. 150 degrees
  3. 180 degrees
  4. 120 degrees

Questions & Step-by-Step Solutions

If two lines are parallel and the transversal creates an angle of 30 degrees with one of the lines, what is the measure of the same-side interior angle?
  • Step 1: Understand that parallel lines are lines that never meet and are always the same distance apart.
  • Step 2: Identify the transversal, which is a line that crosses the two parallel lines.
  • Step 3: Recognize that when the transversal crosses the parallel lines, it creates angles.
  • Step 4: Note that one of the angles formed is 30 degrees.
  • Step 5: Remember that same-side interior angles are the angles that are on the same side of the transversal and between the two parallel lines.
  • Step 6: Understand that same-side interior angles are supplementary, meaning they add up to 180 degrees.
  • Step 7: To find the measure of the same-side interior angle, subtract the known angle from 180 degrees: 180 - 30 = 150 degrees.
  • Step 8: Conclude that the measure of the same-side interior angle is 150 degrees.
  • Parallel Lines and Transversals – Understanding the relationship between parallel lines and angles formed by a transversal, including same-side interior angles.
  • Supplementary Angles – Recognizing that same-side interior angles are supplementary, meaning they add up to 180 degrees.
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