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If two parallel lines are cut by a transversal, what relationship exists between interior angles that are on the same side of the transversal?

Answer :

Final answer:

When two parallel lines are cut by a transversal, the interior angles on the same side of the transversal, known as consecutive interior angles, are supplementary, meaning they add up to 180 degrees. For instance, if one angle measures 70 degrees, the adjacent angle will measure 110 degrees. This relationship is governed by the Consecutive Interior Angles Theorem.


Explanation:

Understanding Angles Formed by Parallel Lines and a Transversal

When two parallel lines are cut by a transversal, specific relationships arise between the angles created. One significant relationship is the behavior of the interior angles that lie on the same side of the transversal. These angles are called consecutive interior angles.

According to the Consecutive Interior Angles Theorem, if two parallel lines are cut by a transversal, then each pair of consecutive interior angles are supplementary. This means that their measures add up to 180 degrees. For example, if one angle measures 70 degrees, the angle directly adjacent to it on the same side of the transversal will measure 110 degrees (since 70 + 110 = 180).

Examples

  • Let Line 1 and Line 2 be parallel, and they are cut by a transversal. If angle A measures 65 degrees, then the angle on the same side of the transversal, angle B, must measure 115 degrees (since 65 + 115 = 180).
  • If you have angles measuring 45 degrees and 135 degrees on the same side of the transversal, they are also consecutive interior angles, confirming that they are supplementary.

In summary, the relationship between consecutive interior angles cut by a transversal through parallel lines is that they are always supplementary angles summing up to 180 degrees.


Learn more about Consecutive Interior Angles here:

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