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

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Question: If two parallel lines are cut by a transversal, and one of the alternate interior angles is 75 degrees, what is the measure of the other alternate interior angle? (2020)

Options:

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

Correct Answer: 75 degrees

Exam Year: 2020

Solution: 

Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, the other alternate interior angle is also 75 degrees.

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

Practice Questions

Q1
If two parallel lines are cut by a transversal, and one of the alternate interior angles is 75 degrees, what is the measure of the other alternate interior angle? (2020)
  1. 75 degrees
  2. 105 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 75 degrees, what is the measure of the other alternate interior angle? (2020)
  • Step 1: Identify the two parallel lines and the transversal that cuts through them.
  • Step 2: Recognize that alternate interior angles are the angles that are on opposite sides of the transversal and inside the parallel lines.
  • Step 3: Note that when two parallel lines are cut by a transversal, alternate interior angles are equal.
  • Step 4: Since one of the alternate interior angles is given as 75 degrees, the other alternate interior angle must also be 75 degrees.
  • Alternate Interior Angles – When two parallel lines are intersected by a transversal, the pairs of alternate interior angles are equal.
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