What is the sum of the measures of complementary angles?

The sum of the measures of complementary angles is defined as 90 degrees. Complementary angles are two angles whose measures add up to 90 degrees. This concept is foundational in geometry and applies to various mathematical contexts, including trigonometry and measurements in polygons.

Understanding the relationships between angles is crucial, as it lays the groundwork for more complex studies involving angles, such as in right triangles. For example, if one angle measures 30 degrees, the complement would measure 60 degrees, since 30 + 60 equals 90 degrees. This property of complementary angles is routinely used in solving problems that involve angles in various geometric figures.

Choosing 180 degrees would suggest angles that are supplementary, which is a different concept altogether, while 360 degrees would imply a full rotation (a complete circle), and 270 degrees does not relate to the definition of complementary angles any further. Thus, identifying that complementary angles sum to 90 degrees is essential for a strong understanding of angle relationships in geometry.