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Precalculus: Homework Help Resource11 chapters | 88 lessons

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Lesson Transcript

Instructor:
*Cathryn Jackson*

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

There are five major types of angle pairs in geometry. In this lesson, you'll explore the different types of angles and learn the rules of measuring those angles. When you finish the lesson, test your knowledge with a short quiz.

There are five major types of angle pairs in geometry. Let's go through them and learn their rules for measuring.

**Complementary angles** are very recognizable because you can make an L shape out of the two angle pairs. This is because complementary angles, when added together, form a right angle, or 90 degrees.

Here, angle ABC and angle CBD are complementary. But, angles can be complementary even if they aren't sitting right next to one another. Here, angle ABE is 45 degrees and angle CBD is 45 degrees, and together they add up to 90 degrees, which means they're complementary. As long as their measurements add up to 90 degrees, they are complementary angle pairs.

**Linear pairs** are angles that form a straight line. They share a common point, and the lines (or rays) they don't share form a straight line.

**Supplementary angles** are angles that add up to 180 degrees. Angles that are 180 degrees look like a straight line. In the illustration here, you can see that supplementary angles can be linear and non-linear angle pairs. As noted, linear pairs of supplementary angles are connected at a common point to form a straight line. In the case of the non-linear pairs, the angles add up to 180 degrees but aren't connected in a straight line.

Try making an X out of two sticks, pencils, or rulers, or anything you can find that is somewhat straight. Now, using a compass, measure each of the four angles in that X shape. Move the sticks closer together, making a wide X, or further apart, making a tall X. Measure the angles again. Notice a pattern? The angles across from one another should have the same measurement. These angles are called **vertical angles**, and one of their properties is that they are congruent, which means that no matter how much you move that X around, the angles across from one another will always have the same measurement in degrees.

In the example here, angles ACB and ECB are vertical, and therefore congruent, angles.

**Adjacent angles** are basically angles that are sitting right next to each other. They share a point, called a vertex, and a side. Adjacent angles are not necessarily congruent, they are just next to one another.

There are five major categories of angles:

**Complementary angles:**angles that, when added together, form a right angle

**Linear pairs:**angles that are next to each other and form a straight line

**Supplementary angles:**angles that add up to 180 degrees

**Vertical angles:**angles located across from one another will always have the same measurement in degrees and be congruent

**Adjacent angles:**angles that are sitting right next to each other and share a vertex and a side

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Precalculus: Homework Help Resource11 chapters | 88 lessons

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