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For the diagram below, if < 3 and < 6 are supplementary, then lines a and b are parallel. What would be the reason for this statement?

For the diagram below, if < 3 and < 6 are supplementary, then lines a and b-example-1
User DanCat
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Answer:

Option D - Consecutive interior angles are supplementary.

Step-by-step explanation:

As we can see in the diagram, ∠3 and ∠6 are interior angles because both are found inside the two lines.

Since both angles are found on the same side of the transversal t, then they are not alternating interior angles instead, the two angles are consecutive interior angles.

Based on the Converse of Consecutive Interior Angle Theorem, if a transversal line intersects two lines and a pair of consecutive interior angles are supplementary, then the two lines are parallel. Therefore, the reason for the given statement is Option D - Consecutive interior angles are supplementary.

User Dido
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