Vertical angles are never:
(A) complementary
(B) supplementary
(C) right angles
(D) adjacent
(E) congruent
The correct answer and explanation is:
The correct answer is (D) adjacent.
Vertical angles are formed when two lines intersect. At the point of intersection, two pairs of opposite angles are created. These opposite angles are always congruent to each other, meaning they have the same measure.
Now, let’s break down the other choices:
- Complementary angles are two angles that add up to 90 degrees. Vertical angles do not have a fixed sum, so they are not necessarily complementary. They can be complementary if their measures happen to add up to 90 degrees, but that is not a rule for vertical angles.
- Supplementary angles are two angles that add up to 180 degrees. Like complementary angles, vertical angles are not inherently supplementary. However, vertical angles may be supplementary in certain cases if their measures sum to 180 degrees, but this is not a defining characteristic.
- Right angles are angles of exactly 90 degrees. Vertical angles do not have to be right angles. They can be any angle, as long as they are opposite each other at the intersection of two lines.
- Adjacent angles are angles that share a common side and vertex. Vertical angles, by definition, are not adjacent because they are opposite each other, meaning they do not share a common side. This is why vertical angles are never adjacent.
- Congruent angles means angles that have the same measure. Vertical angles are always congruent by definition. This is a fundamental property of vertical angles: they are equal in measure.
So, the correct choice is (D) adjacent because vertical angles cannot be adjacent. They are always opposite each other and congruent, but they never share a common side.