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If two lines are parallel and the transversal creates an exterior angle of 120 d

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Question: If two lines are parallel and the transversal creates an exterior angle of 120 degrees, what is the measure of the corresponding interior angle?

Options:

  1. 60 degrees
  2. 120 degrees
  3. 180 degrees
  4. 90 degrees

Correct Answer: 60 degrees

Solution: 

The corresponding interior angle is supplementary to the exterior angle, so it measures 60 degrees.

If two lines are parallel and the transversal creates an exterior angle of 120 d

Practice Questions

Q1
If two lines are parallel and the transversal creates an exterior angle of 120 degrees, what is the measure of the corresponding interior angle?
  1. 60 degrees
  2. 120 degrees
  3. 180 degrees
  4. 90 degrees

Questions & Step-by-Step Solutions

If two lines are parallel and the transversal creates an exterior angle of 120 degrees, what is the measure of the corresponding interior angle?
  • 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 an exterior angle is formed outside the parallel lines when the transversal crosses them.
  • Step 4: Note that the exterior angle given in the question is 120 degrees.
  • Step 5: Remember that corresponding interior angles are supplementary to exterior angles, meaning they add up to 180 degrees.
  • Step 6: To find the corresponding interior angle, subtract the exterior angle from 180 degrees: 180 - 120 = 60 degrees.
  • Step 7: Conclude that the measure of the corresponding interior angle is 60 degrees.
  • Parallel Lines and Transversals – When a transversal crosses parallel lines, it creates corresponding angles that are equal and alternate interior angles that are equal, as well as exterior angles that are supplementary to interior angles.
  • Supplementary Angles – Two angles are supplementary if their measures add up to 180 degrees.
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