Introduction to Angles

We begin our study of angles by learning what they are, how to name them, and ways in which angles can be classified. These concepts are explained below.


An angle is formed when two rays meet at a common endpoint, or vertex. The two sides of the angle are the rays, and the point that unites them is called the vertex.

The vertices are shown in red in the diagram above

Naming Angles

Angles can be named in various ways. One way is to use the ? symbol accompanied by three letters. The first and third letters indicate points on the two rays. The letter in the middle is the vertex. Note that the first and third letters are interchangeable because they both measure the same angle. Another way to label an angle is by just using the ? symbol accompanied by the vertex point alone. However, this method only works when there is only one angle at the vertex point. If more than one angle is formed at a vertex point, we need to specify which angle we are talking about by naming it in a different way. Finally, the last way to label an angle is by using the ? symbol accompanied by the letter or number shown between the angle. The different ways of labeling an angle are shown below.

The angle above can be called ?ABC, ?CBA, ?B, or ??

Classifications of Angles

Angles can be measured in degrees or radians. For the time being, we will strictly talk about angles in terms of their degree measure. The symbol for degrees is °. Angles can measure from 0° up to 360°. Angles with no measure are called zero angles, while angles of 360° are full rotations. For our study of geometry, we will primarily focus on three important classifications of angles: acute, obtuse, and right.

Right Angle

A right angle is an angle whose measure is exactly 90°. An easy way to determine whether an angle is a right angle is by considering whether a small square could fit perfectly in the corner of the intersection of the two lines that form the angle. While you would need a protractor to give a more precise measurement, this can give you an approximation of whether or not an angle is close to 90°.

Acute Angle

An acute angle is an angle whose measure is less than 90°. For these kinds of angles, a square could not fit perfectly at the intersection of the two lines that form them.

Obtuse Angle

Obtuse angles have measures greater than 90° but less than 180°.

Straight Angle

If an angle's measure is 180°, it is called a straight angle. Straight angles are just lines with three points on them.

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