Answer:
C. Vertical angles
Explanation:
Given angles 5 and 8 where line c crosses line a, you want to know what type they are.
Crossing lines
Where two lines cross, four angles are formed. They all share the vertex point where the lines intersect. If they share a side (and no interior space), they are adjacent angles that form a linear pair. As such, they are supplementary.
In the given figure the supplementary angle pairs where line c crosses line a are ...
(5, 6), (6, 8), (7, 8), (5, 7)
If the angles do not share a side, but are formed from opposite rays, they are "vertical angles" and are congruent.
The vertical angle pairs there are ...
(5, 8), (6, 7)
Angles 5 and 8 are vertical angles, choice C.
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Additional comment
Angle pairs (1, 8) and (2, 7) are "alternate exterior angles." Angle pairs (3, 6) and (4, 5) are "alternate interior angles."
Assuming lines b and c are parallel, considering also angles where line b crosses line a, there are additional supplementary pairs of angles:
(1, 2), (2, 4), (3, 4), (1, 3), (1, 6), (1, 7), (2, 5), (2, 8), (3, 5), (3, 8), (4, 6), (4, 7)
When parallel lines are crossed by a transversal, all of the acute angles are congruent, all of the obtuse angles are congruent, and the acute angles are supplementary to the obtuse angles. The angles are referred to by different names (and different theorems), depending on where they are in relation to the transversal and the parallel lines.
The problem here is mostly concerned with vocabulary. The "how to do this" is "learn the vocabulary."
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