# Angles

## Overview

Expect to see questions that test your understanding of angles and their properties. In this section we’ll cover the following:

• Angle Basics
• Classifying Angles by Size
• Classifying Angles Relationships
• Identifying Angle Properties in Other Geometric Figures

Let’s look at each of these in more detail:

### Angle Basics

What is an angle? Look at this definition.

To review angle basics, click on this link. It is a presentation that goes over this topic.

### Classifying Angles by Size

Angles range from 0° to 360°. Depending on the measure of the angle, it can fall into several categories of angles.

• An angle whose measure is less than 90° is an acute angle.

• An angle greater than 90° and less than 180° is an obtuse angle.

• An angle that measures 90° is a right angle.

• An angle greater than 180° and less than 360° is called a reflex angle

• An angle that is 180° is called a straight angle

To learn more about classifying triangles by angle measures, click on this link. It is a presentation that goes over this topic.

### Classifying Angles Relationships

Angles can be classified by their angle measure. Often angles are associated with other angles. For example, two angles can share a side:

Angles make up the interior of polygons:

Or, when two lines intersect, four angles are formed:

Take a look at this link to see a presentation on these different angle relationships. In particular, make sure you understand the following types of angle relationships:

• Complementary Angles
• Supplementary Angles
• Vertical Angles

A special case of angle relationships happens when two parallel lines are cut by a transversal.

Click on this link to see a presentation that shows all the angles formed by this configuration. Make a note of the congruent and supplementary angles formed.

 SAT Skill: Angle Properties Example 1 Given the triangle below, find x. Because the lines are perpendicular to each other, then the triangle is a right triangle, as shown here. That means that the two acute angles of the right triangle are complementary. So, we can write an equation to solve for x: Example 2 Given the parallel lines below, find x. The two parallel lines are cut by a transversal. The two angles shown are supplementary to each other. Now you can write an equation and solve for x:

### Identifying Angle Properties in Other Geometric Figures

Make sure you are familiar with key triangle theorems that relate to angle measures. They will often be part of solving a particular SAT problem involving triangles.

Click on this link to see a slide show of these theorems.

 SAT Skill: Triangle Properties Example 1 Given these triangles, what is the value of x? Given that two corresponding sides and an included angle are congruent, then we can conclude that the two angles are congruent using the SAS Theorem.   The exterior angle (115°) is supplementary to angle ABC. This corresponding angle is found on the second triangle. We can now write and solve an equation for x:   Example 2 Given these triangles, what is the value of x? Use the Exterior Angle Theorem to generate another equation: Use the two equations to solve a system: