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If two lines are parallel and the measure of one of the interior angles is 45 de

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

Options:

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

Correct Answer: 135 degrees

Solution: 

Interior angles on the same side of the transversal are supplementary, so 180 - 45 = 135 degrees.

If two lines are parallel and the measure of one of the interior angles is 45 de

Practice Questions

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

Questions & Step-by-Step Solutions

If two lines are parallel and the measure of one of the interior angles is 45 degrees, what is the measure of the other interior angle on the same side of the transversal?
  • Step 1: Understand that parallel lines are lines that never meet and are always the same distance apart.
  • Step 2: Identify that a transversal is a line that crosses two or more other lines.
  • Step 3: Recognize that when a transversal crosses parallel lines, it creates interior angles.
  • Step 4: Note that interior angles on the same side of the transversal are called 'supplementary angles.'
  • Step 5: Remember that supplementary angles add up to 180 degrees.
  • Step 6: Since one of the interior angles is 45 degrees, subtract this from 180 degrees to find the other angle.
  • Step 7: Calculate: 180 - 45 = 135 degrees.
  • Step 8: Conclude that the measure of the other interior angle on the same side of the transversal is 135 degrees.
  • Parallel Lines and Transversals – When two parallel lines are intersected by a transversal, certain angle relationships are established, including corresponding angles, alternate interior angles, and interior angles on the same side of the transversal.
  • Supplementary Angles – Two angles are supplementary if their measures add up to 180 degrees. This is particularly relevant for interior angles on the same side of a transversal when dealing with parallel lines.
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