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Angle Word Problems Study Guide

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Updated on Oct 3, 2011

Introduction to Angle Word Problems

The composer opens the cage door for arithmetic, the draftsman gives geometry its freedom.

—COCTEAU (1839–1963)

This lesson will review the basic terms of geometry and list the special types of angles and angle pairs found in many geometry word problems.

Basic Figures of Geometry

Knowing the basic terms of geometry can make the study of more complicated shapes much easier. Listed next are a few of these basic terms.

      A point is a location in space.
      A line is an infinite collection of points extending in opposite directions.
      A plane is a never-ending flat surface that extends in all directions.
      A ray is the set of all points extending in a straight line from one side of an endpoint.

Angles

An angle is made up two rays that meet at a common endpoint. The rays are the sides of the angle, and the common endpoint is the vertex of the angle.

Angles can be named in various ways. They can be named by the letter of the vertex, by three letters with the middle letter being the vertex, or by a number written in the interior of the angle. These three ways to name angles () are shown in the following figure.

Angles

Tip:

Here are some important types of angles and their measures:

      Acute angles measure less than 90°.
      Right angles measure 90°.
      Obtuse angles measure greater than 90 but less than 180°.
      Straight angles measure 180°.
      Reflex angles measure more than 180°.

There are special types of pairs of angles that are common to geometry word problems. These special types are explained next.

Adjacent Angles

Adjacent angles are angles next to each other that share a common ray, or side, and a common vertex. Nonadjacent angles are not next to each other and do not share a common ray, or side. An example of each is shown below.

Adjacent Angles

Vertical Angles

Vertical angles are the nonadjacent angles formed by two intersecting lines. The measures of vertical angles are always equal.

Look at the following example. The measure of angles 1 and 3 are each 60°; they are vertical angles. The measure of angles 2 and 4 are each 120°; they are also a vertical pair of angles. Notice that the adjacent angles have a sum of 120 + 60 = 180°.

Vertical Angles

Complementary and Supplementary Pairs of Angles

Complementary angles are two angles that have a sum of 90°. They can be adjacent, or nonadjacent angles, as shown next.

Complementary and Supplementary Pairs of Angles

Supplementary angles are two angles that have a sum of 180°. They can be adjacent, or nonadjacent angles, as shown next. If two supplementary angles are also adjacent, they are known as a linear pair.

Complementary and Supplementary Pairs of Angles

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