# Why are supplementary angles important?

Supplementary angles are important because they can be used to find other angles.

For example, if given the below problem and told that angle 1 equals 100˚, we could use supplementary angle that sum to 180 to determine all of the other angles.

Angles 1 and 2 are supplementary, so 180-angle 1 is equal to angle 2. Knowing angle to is therefore 80˚, we can continue using supplementary angles to find all other values.

Problems like this would not be possible without the proofs of supplementary angles.

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Supplementary angles are important because they help in solving geometric problems, particularly those involving angles. Understanding supplementary angles allows us to determine relationships between angles in various geometric figures, such as triangles, quadrilaterals, and polygons. They are crucial in trigonometry, where knowledge of angles is essential for solving problems related to measurements, distances, and navigation. Additionally, supplementary angles play a significant role in the study of parallel lines and transversals, as well as in proving geometric theorems and properties. Overall, understanding supplementary angles enhances our ability to analyze geometric configurations and solve mathematical problems efficiently.

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