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If two lines are parallel and the transversal creates an interior angle of 75 de

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Question: If two lines are parallel and the transversal creates an interior angle of 75 degrees, what is the measure of the alternate interior angle?

Options:

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

Correct Answer: 75 degrees

Solution: 

Alternate interior angles are equal when two parallel lines are cut by a transversal.

If two lines are parallel and the transversal creates an interior angle of 75 de

Practice Questions

Q1
If two lines are parallel and the transversal creates an interior angle of 75 degrees, what is the measure of the alternate interior angle?
  1. 75 degrees
  2. 105 degrees
  3. 90 degrees
  4. 180 degrees

Questions & Step-by-Step Solutions

If two lines are parallel and the transversal creates an interior angle of 75 degrees, what is the measure of the alternate interior angle?
  • Step 1: Identify the two parallel lines and the transversal line that crosses them.
  • Step 2: Note the interior angle created by the transversal and one of the parallel lines, which is given as 75 degrees.
  • Step 3: Understand that alternate interior angles are the angles that are on opposite sides of the transversal and inside the parallel lines.
  • Step 4: Remember the property that states alternate interior angles are equal when two lines are parallel.
  • Step 5: Since the given angle is 75 degrees, the alternate interior angle must also be 75 degrees.
  • Alternate Interior Angles – When two parallel lines are intersected by a transversal, the alternate interior angles are equal.
  • Transversal – A transversal is a line that crosses at least two other lines, creating various angles.
  • Parallel Lines – Parallel lines are lines in a plane that do not meet; they are always the same distance apart.
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