A complementary angle is defined as two angles whose measures add up to 90 degrees. For example, if one angle measures 30 degrees, its complementary angle would measure 60 degrees because 30 + 60 = 90. Complementary angles can be found in various geometric shapes and are often used in trigonometry. These angles can be adjacent, meaning they share a common vertex and side, or they can be separate. Understanding complementary angles is essential in fields like geometry, architecture, and engineering, where precise angle measurements are crucial for design and construction.