Understanding Complementary Angles: Definition, Examples, and Applications in Geometry and Trigonometry

Complementary angles Chapter 1 (p. 46)

Complementary angles are pairs of angles whose measures sum up to 90 degrees

Complementary angles are pairs of angles whose measures sum up to 90 degrees. In other words, when you add the measures of two complementary angles together, they will always result in 90 degrees.

For example, let’s say we have angle A and angle B. If angle A measures 30 degrees, then angle B would be the complement of angle A, as its measure would be 90 – 30 = 60 degrees. Similarly, if angle A measures 45 degrees, then angle B would measure 90 – 45 = 45 degrees as well.

Complementary angles are often represented by the symbols ⊥ (perpendicular) or ∠ (angle). So, if angle A and angle B are complementary, we can denote it as ∠A ⊥ ∠B.

It’s important to note that complementary angles do not have to be adjacent or next to each other. They can be anywhere in a figure or even in different parts of a problem.

Complementary angles are commonly encountered in geometry and trigonometry problems. They have several applications, including calculating missing angles or solving for unknown variables in a given figure or problem.

For example, if we have a right triangle with one angle measuring 30 degrees, we can find the measure of the other acute angle by subtracting 30 from 90 (since the sum of all angles in a triangle is always 180 degrees). Therefore, the other angle would be 90 – 30 = 60 degrees. These two angles are complementary, as their measures add up to 90 degrees.

Knowing the concept of complementary angles can also be useful in real-life scenarios. For instance, if you have a right-angle mirror, the angle between the mirror and the surface it is placed on will always be complementary to the angle of reflection.

In summary, complementary angles are two angles whose measures add up to 90 degrees. They are often used in geometry and trigonometry to solve for missing angles or variables in various problems and figures.

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