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A complementary angle is an angle that, when added to another angle, equals 90 degrees, or a right angle. In other words, two angles are complementary if their sum is a right angle. This concept of complementary angles is basic and fundamental in geometry, trigonometry, and other fields of mathematics.

For example, if one angle measures 30 degrees, the complementary angle will measure 60 degrees. Similarly, if one angle measures 45 degrees, the complementary angle will be 45 degrees as well. This is because the two angles add up to a right angle, which is always equal to 90 degrees.

Complementary angles are often used in practical applications involving angles and measurements. A classic example is a right triangle, where one of the angles measures exactly 90 degrees. The other two angles are always complementary, and their measurements determine the proportions and properties of the triangle.

In trigonometry, complementary angles play a crucial role in the definition and calculation of trigonometric functions such as sine, cosine, tangent, and their inverses. These functions express the ratios between the sides of a right triangle and the angles opposite or adjacent to them.

Complementary angles can also be used in the study of angles and lines in space, such as in aviation, navigation, architecture, and engineering. They provide a common reference point and an intuitive way to measure and compare angles and distances.

In summary, a complementary angle is an angle that adds up to 90 degrees, or a right angle. It is an essential concept in geometry, trigonometry, and other fields of mathematics, as well as in practical applications involving angles and measurements. Understanding and using complementary angles can help us solve problems, design structures, and navigate the world around us.