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Answer:
C. The statement is sometimes true
Step-by-step explanation:
When one line crosses another, it forms 4 angles. They can be considered as ...
4 pairs of supplementary angles, or
2 pairs of congruent (vertical) angles
Hence when a transversal crosses parallel lines, two such sets are produced. In the special case that two of the vertical angles measure 45°, they will be complementary. There will be a total of six pairs of complementary angles in that case, which is to say that 4 pairs of complementary angles are formed along with two other pairs.
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Additional comment
Consider two horizontal parallel lines, and a transversal that extends downward to the right. At each intersection, let angles be numbered consecutively starting with 1 at the top left and working clockwise around first the top intersection, then the bottom intersection. Then congruent acute angles are 1, 3, 5, 7. If these angles are all 45°, then the pairs of complementary angles are {1, 3}, {1, 5}, {1, 7}, {3, 5}, {3, 7}, {5, 7}. Respectively, these pairs are identified as vertical, corresponding, alternate exterior, alternate interior, corresponding, vertical. The four pairs that are not vertical angles are created only by the intersection of a transversal with parallel lines.
Your teacher may argue "never true," which is not an unreasonable take on this situation.
