Types of Angles Study Guide

Introduction to Types of Angles

Lesson Summary

This lesson will teach you how to classify and name several types of angles. You will also learn about opposite rays.

Many of us use the term angle in everyday conversations. For example, we talk about camera angles, angles for pool shots and golf shots, and angles for furniture placement. In geometry, an angle is formed by two rays with a common endpoint. The symbol used to indicate an angle is . The two rays are the sides of the angle. The common endpoint is the vertex of the angle. In the following figure, the sides are and , and the vertex is R.

Naming Angles

People call you different names at different times. Sometimes, you are referred to by your full name, and other times, only by your first name or maybe even a nickname. These different names don't change who you are—just the way in which others refer to you. You can be named differently according to the setting you're in. For example, you may be called your given name at work, but your friends might call you by a nickname. Confusion can sometimes arise when these names are different.

Just like you, an angle can be named in different ways. The different ways an angle can be named may be confusing if you do not understand the logic behind the different methods of naming.

If three letters are used to name an angle, then the middle letter always names the vertex. If the angle does not share the vertex point with another angle, then you can name the angle with only the letter of the vertex. If a number is written inside the angle that is not the angle measurement, then you can name the angle by that number. You can name the following angle any one of these names: WET, TEW, E, or 1.

Right Angles

Angles that make a square corner are called right angles (see p. 26 for more details about what makes an angle a right angle). In drawings, the following symbol is used to indicate a right angle:

Straight Angles

Opposite rays are two rays with the same endpoint that form a line. They form a straight angle. In the following figure, and are opposite rays.

Classifying Angles

Angles are often classified by their measures. The degree is the most commonly used unit for measuring angles. One full turn, or a circle, equals 360°.

Acute Angles

An acute angle has a measure between 0° and 90°. Here are two examples of acute angles:

Right Angles

A right angle has a 90° measure. The corner of a piece of paper will fit exactly into a right angle. Here are two examples of right angles:

Obtuse Angles

An obtuse angle has a measure between 90° and 180°. Here are two examples of obtuse angles:

Straight Angles

A straight angle has a 180° measure. ABC is an example of a straight angle:

Practice problems for these concepts can be found at: Types of Angles Practice Questions.