Supplementary Angles

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In geometry, supplementary angles are two angles whose measures add up to 180 degrees. Supplementary angles are often denoted with the symbol "∠" followed by two letters to represent the angles. For example, if angles A and B are supplementary, they can be written as ∠A + ∠B = 180°.

Various different types of figures, such as triangles, quadrilaterals, and other polygons, comprise supplementary angles. They are most often used in geometry to prove that particular figures are similar or congruent or to locate missing angle measurements.

There are several different types of supplementary angles:

  • Adjacent supplementary angles are two angles that share a common vertex and a common side but have no other sides in common. They are supplementary because the measure of one angle is equal to 180 degrees minus the measure of the other angle.
  • Linear pair supplementary angles are two adjacent angles whose non-common sides are opposite rays. They are supplementary because the measures of the two angles add up to 180 degrees.
  • Exterior angles of a triangle are the angles formed by extending one side of a triangle to create a new triangle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles (the angles not adjacent to the exterior angle).

In many real-world applications, like engineering and construction, in which they are used to create structures, supplementary angles play a significant role. They are a subject of study in trigonometry and geometry as well.

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