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In a pair of parallel lines cut by a transversal, if one of the interior angles

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Question: In a pair of parallel lines cut by a transversal, if one of the interior angles is 120°, what is the measure of the other interior angle on the same side of the transversal?

Options:

  1. 60°
  2. 120°
  3. 180°
  4. 90°

Correct Answer: 60°

Solution: 

The two interior angles on the same side of the transversal are supplementary, so the other angle is 180° - 120° = 60°.

In a pair of parallel lines cut by a transversal, if one of the interior angles

Practice Questions

Q1
In a pair of parallel lines cut by a transversal, if one of the interior angles is 120°, what is the measure of the other interior angle on the same side of the transversal?
  1. 60°
  2. 120°
  3. 180°
  4. 90°

Questions & Step-by-Step Solutions

In a pair of parallel lines cut by a transversal, if one of the interior angles is 120°, what is the measure of the other interior angle on the same side of the transversal?
  • Step 1: Understand that a transversal is a line that crosses two parallel lines.
  • Step 2: Identify that when a transversal cuts parallel lines, it creates pairs of interior angles on the same side.
  • Step 3: Know that the two interior angles on the same side of the transversal are supplementary, meaning they add up to 180°.
  • Step 4: Since one of the angles is given as 120°, set up the equation: Angle 1 + Angle 2 = 180°.
  • Step 5: Substitute the known angle into the equation: 120° + Angle 2 = 180°.
  • Step 6: Solve for Angle 2 by subtracting 120° from 180°: Angle 2 = 180° - 120°.
  • Step 7: Calculate the result: Angle 2 = 60°.
  • Supplementary Angles – Two angles that add up to 180° are called supplementary angles, which is a key property when dealing with parallel lines cut by a transversal.
  • Transversal and Parallel Lines – A transversal is a line that intersects two or more lines, creating various angles, including corresponding, alternate interior, and interior angles.
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