Answer :
Final answer:
In mathematics, complementary angles add up to 90 degrees, supplementary angles add up to 180 degrees, and vertical angles are equal and formed when two lines intersect. Should none of these relationships apply, the answer is D> 'none of these'.
Explanation:
In the study of mathematics, especially geometry, complementary, supplementary, and vertical are terms used to show relationships between angles. Complementary angles are two angles that add up to 90 degrees. In contrast, supplementary angles are two angles that add up to 180 degrees. Vertical angles are formed when two lines intersect and are directly across from each other. They are always congruent or equal. If the pair of angles have no such relationships, that is, they do not meet any of these conditions, then the response is 'none of these'.
For example, if you have a pair of angles that measures 30 and 60 degrees respectively, they are complementary because they add up to 90 degrees. If another pair of angles measures 120 and 60 degrees, they are supplementary because they add up to 180 degrees. If you have two angles formed by intersecting lines and they both measure 80 degrees, they are vertical angles.
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