Adjacent Angles

Topic

Angles

Definition

Adjacent angles are two angles that share a common vertex and side, but do not overlap.

Description

Adjacent angles are commonly encountered in geometric figures and are crucial for understanding angle relationships. They are often used in the study of polygons, where the sum of adjacent angles can help determine the properties of the shape. In real-world applications, adjacent angles are important in construction and engineering, where precise angle measurements ensure that components fit together correctly. For example, when constructing a staircase, the angles between the steps and the floor must be carefully calculated. In math education, adjacent angles help students understand angle addition and the properties of intersecting lines, contributing to a comprehensive understanding of geometry.

For a complete collection of terms related to Angles click on this link: Angles Collection.

What Are Angles?

In this illustration two rays intersect at a point. Points A and B are on one ray and points B and C are on another ray. These two rays form an angle.

The angle is the corner sweep formed by the two rays. Rays BA and BC form Angle ABC. 

Point B is the vertex of the angle. The vertex is the corner formed by the angle.

Angles can also be formed by intersecting lines. In this case four angles are formed when lines intersect.

The same happens when two line segments intersect, as shown below.

Geometric shapes are sometimes defined by the number of angles they have.

Even circles can contain angles, as shown below.

How Are Angles Measured?

Angles are measured in degrees or in radians. In this illustration, Angle ABC is a 30° angle.

Angles are also measured in radians. Radian measures are useful for indicating the portion of a circle an angle sweeps.

Use a protractor to measure an angle.

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