What does it mean for two angles to be complementary?

When two angles are described as complementary, it means that the sum of their measures is exactly 90 degrees. This is a fundamental concept in geometry that helps in understanding the relationships between different types of angles. Complementary angles can take various forms; for example, one angle could be 30 degrees while the other is 60 degrees, and their combination would still fulfill the requirement of adding to 90 degrees.

The significance of this relationship is particularly important in many geometric principles, including right triangles and various properties of polygons. In contrast, angles that add up to 180 degrees are classified as supplementary, which represents a different concept entirely. While it's true that complementary angles can often be acute (less than 90 degrees), they do not have to be both acute to fulfill the condition of being complementary; one angle could be more than 90 degrees while the other is less, but their total must still equal 90 degrees to meet the requirement. The definition doesn't hinge on one angle measuring more than another or both angles being acute. Thus, the definition aligning with the requirement of summing to 90 degrees clearly establishes the meaning of complementary angles.