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If two parallel lines are cut by a transversal and one of the alternate interior

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Question: If two parallel lines are cut by a transversal and one of the alternate interior angles is 120 degrees, what is the measure of the other alternate interior angle?

Options:

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

Correct Answer: 120 degrees

Solution: 

By the Alternate Interior Angles Theorem, alternate interior angles are equal. Thus, the other alternate interior angle also measures 120 degrees.

If two parallel lines are cut by a transversal and one of the alternate interior

Practice Questions

Q1
If two parallel lines are cut by a transversal and one of the alternate interior angles is 120 degrees, what is the measure of the other alternate interior angle?
  1. 60 degrees
  2. 120 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 alternate interior angles is 120 degrees, what is the measure of the other alternate interior angle?
  • Step 1: Identify the two parallel lines and the transversal that cuts through them.
  • Step 2: Locate the alternate interior angles formed by the transversal and the parallel lines.
  • Step 3: Note that one of the alternate interior angles is given as 120 degrees.
  • Step 4: Recall the Alternate Interior Angles Theorem, which states that alternate interior angles are equal when two parallel lines are cut by a transversal.
  • Step 5: Since one alternate interior angle is 120 degrees, the other alternate interior angle must also be 120 degrees.
  • Alternate Interior Angles Theorem – This theorem states that when two parallel lines are cut by a transversal, the pairs of alternate interior angles are equal.
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