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Given two parallel lines cut by a transversal, if one of the same-side interior

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Question: Given two parallel lines cut by a transversal, if one of the same-side interior angles is 40 degrees, what is the measure of the other same-side interior angle?

Options:

  1. 40 degrees
  2. 140 degrees
  3. 180 degrees
  4. 90 degrees

Correct Answer: 140 degrees

Solution: 

Same-side interior angles are supplementary. Therefore, if one angle is 40 degrees, the other must be 180 - 40 = 140 degrees.

Given two parallel lines cut by a transversal, if one of the same-side interior

Practice Questions

Q1
Given two parallel lines cut by a transversal, if one of the same-side interior angles is 40 degrees, what is the measure of the other same-side interior angle?
  1. 40 degrees
  2. 140 degrees
  3. 180 degrees
  4. 90 degrees

Questions & Step-by-Step Solutions

Given two parallel lines cut by a transversal, if one of the same-side interior angles is 40 degrees, what is the measure of the other same-side interior angle?
  • Step 1: Understand that same-side interior angles are the angles that are on the same side of the transversal and between the two parallel lines.
  • Step 2: Remember that same-side interior angles are supplementary, which means they add up to 180 degrees.
  • Step 3: If one of the same-side interior angles is 40 degrees, write it down: Angle 1 = 40 degrees.
  • Step 4: To find the measure of the other same-side interior angle (Angle 2), use the formula: Angle 1 + Angle 2 = 180 degrees.
  • Step 5: Substitute the known value into the equation: 40 degrees + Angle 2 = 180 degrees.
  • Step 6: Solve for Angle 2 by subtracting 40 degrees from both sides: Angle 2 = 180 degrees - 40 degrees.
  • Step 7: Calculate the result: Angle 2 = 140 degrees.
  • Same-Side Interior Angles – Same-side interior angles are formed when a transversal intersects two parallel lines and are supplementary, meaning their measures add up to 180 degrees.
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