Understanding Supplementary Angles | Definition, Equations, and Applications in Geometry and Trigonometry

Supplementary Angles

Supplementary angles are a pair of angles that add up to 180 degrees

Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles, and the sum of their measures equals 180 degrees, then they are supplementary angles.

Suppose we have two angles, angle A and angle B. If angle A measures x degrees, and angle B measures y degrees, then angle A and angle B are supplementary if the following equation is true:

x + y = 180

For example, if angle A measures 70 degrees, then angle B must measure 110 degrees in order for them to be supplementary (70 + 110 = 180). Similarly, if angle A measures 120 degrees, angle B must measure 60 degrees (120 + 60 = 180).

Supplementary angles can be found in various geometric configurations. For instance, when two lines intersect, opposite angles formed by the intersection are always supplementary. These are known as vertical angles. Additionally, two adjacent angles that form a straight line, also known as a straight angle, are supplementary as well.

Knowing that two angles are supplementary can be useful in solving problems involving geometry and trigonometry. By recognizing the relationship between angles, we can use the concept of supplementary angles to find missing angle measures or solve equations involving angles.

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