In geometry, complementary angles are two angles whose measures add up to 90 degrees. For example, if one angle measures 30 degrees, its complementary angle would measure 60 degrees. This concept is important in various applications, including trigonometry and design. On the other hand, supplementary angles are two angles that sum to 180 degrees. For instance, if one angle is 110 degrees, the supplementary angle would be 70 degrees. Understanding these relationships helps in solving problems related to triangles, polygons, and other geometric figures.