Complementary Angles

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Complementary angles in geometry are two angles whose measures sum to 90 degrees. Complementary angles are more often represented by the symbol "∠" followed by two letters. For instance, angles A and B can be written as ∠A + ∠B = 90° if they are complementary.

Numerous different types of figures, such as triangles, quadrilaterals, and other polygons, contain complementary angles. They are often used in geometry to determine missing angle measurements or to demonstrate the similarity or congruence of particular figures.

There are several different types of complementary angles:

  • Adjacent complementary angles are two angles that share a common vertex and a common side but have no other sides in common. They are complementary because the measure of one angle is equal to 90 degrees minus the measure of the other angle.
  • Linear pair complementary angles are two adjacent angles whose non-common sides are opposite rays. They are complementary because the measures of the two angles add up to 180 degrees, and 180 degrees - 90 degrees = 90 degrees.
  • Vertical angles are two non-adjacent angles formed by two intersecting lines. They are complementary because the measures of the two angles are always equal (since they are vertical angles).

In many real-world applications, such as engineering and construction, where they are used to create structures, complementary angles play an important role. They are a subject of study in trigonometry and geometry as well.

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