To determine which angles are supplementary to ∠4, we need to identify the angles that, when added to ∠4, equal 180 degrees. Supplementary angles are formed when two angles sit next to each other and add up to 180 degrees.
In the context of parallel lines cut by a transversal, we can observe the following relationships:
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Alternate Interior Angles: These angles are equal. So ∠4 (which is one of the alternate interior angles) is equal to ∠5. Therefore, ∠5 is not supplementary to ∠4.
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Corresponding Angles: These angles are also equal when the lines are parallel. Thus, if ∠4 is a corresponding angle with another angle, they will also not be supplementary.
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Consecutive Interior Angles: These angles are on the same side of the transversal and are supplementary in this context. Thus, ∠4 and ∠6 are consecutive interior angles and therefore supplementary.
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Exterior Angles: Angles on the outside of the parallel lines, such as the alternate exterior angles (1, 8, and 2, 7), are not directly relevant for the supplementary angle consideration with ∠4, unless we check for angles that together with ∠4 makes up 180 degrees.
From the given description, the angle that is supplementary to ∠4 is:
- ∠6 (because it is a consecutive interior angle).
Thus, the angles that are supplementary to ∠4 are:
- ∠6.