What defines complementary angles?

What defines complementary angles?

• A. They are supplementary to vertical angles
• B. They equal 180° when added
• C. They equal 90° when added
• D. They are on the same line

Answer: (C)

Complementary angles are defined as two angles whose measures add up to 90 degrees. This relationship is fundamental in geometry, particularly when dealing with right angles and various shapes. For example, if one angle measures 30 degrees, the angle that complements it will measure 60 degrees, since 30 + 60 = 90. In contrast, the other options present concepts that are not relevant to the definition of complementary angles. Supplementary angles, for instance, are those that add up to 180 degrees, but this does not apply to complementary angles. Additionally, while angles on the same line pertain to adjacent angles and straight angles, they do not define the specific relationship of adding to 90 degrees that characterizes complementary angles. Thus, the definition of complementary angles centers solely on their sum being 90 degrees, making it essential within the study of angle relationships.

Complementary angles are defined as two angles whose measures add up to 90 degrees. This relationship is fundamental in geometry, particularly when dealing with right angles and various shapes. For example, if one angle measures 30 degrees, the angle that complements it will measure 60 degrees, since 30 + 60 = 90.

In contrast, the other options present concepts that are not relevant to the definition of complementary angles. Supplementary angles, for instance, are those that add up to 180 degrees, but this does not apply to complementary angles. Additionally, while angles on the same line pertain to adjacent angles and straight angles, they do not define the specific relationship of adding to 90 degrees that characterizes complementary angles. Thus, the definition of complementary angles centers solely on their sum being 90 degrees, making it essential within the study of angle relationships.