An angle is a plane figure formed by two rays that have the same starting point. This common point is called the vertex of the angle and the rays are the sides of the angle.

There are different ways to denote an angle and all involve the symbol $\angle$ in front of the name. One way is to name an angle by its vertex alone. Alternatively, it can be named by using all three points that make up the angle. In this case, the vertex is always in the middle of the name. Additionally, angles within a diagram can be denoted with numbers or lowercase Greek letters.

Using the Vertex	Using the Vertex and One Point on Each Ray	Using a Number	Using Greek Letters
$\angle B$	$\angle ABC$ or $\angle CBA$	$\angle 1$	$\angle \alpha$ or $\angle \beta$ or $\angle \theta$

The measure of an angle, denoted by $m\angle ,$ is the number of degrees between the rays. It is found by applying the Protractor Postulate. When two angles have the same measure, they are said to be congruent.

Interior and Exterior of an Angle

An angle divides the plane into two parts.

• The region between the sides, or interior of the angle
• The region outside the sides, or exterior of the angle

These regions can be examined in the following graph. Notice that the interior of the angle is the region for which the angle measure is less than $180^{\circ }.$

An acute angle is an angle whose measure is greater than $0^{\circ }$ but less than $90^{\circ }.$ When using radians as the unit of measure, an angle is acute when its measure is greater than $0$ but less than $\frac{\pi }{2},$ or about $1.57,$ radians.

A right angle is an angle whose measure is exactly $90^{\circ }.$ In diagrams, right angles are denoted with a square angle marker. When using radians as the unit of measure, an angle is a right angle when its measure is exactly $\frac{\pi }{2},$ or about $1.57,$ radians.

An obtuse angle is an angle whose measure is greater than $90^{\circ }$ but less than $180^{\circ }.$ When using radians as the unit of measure, an angle is obtuse when its measure is greater than $\frac{\pi }{2},$ or about $1.57,$ but less than $\pi ,$ or about $3.14,$ radians.

A straight angle is an angle whose measure is exactly $180^{\circ }.$ When using radians as the unit of measure, an angle is a straight angle when its measure is equal to $\pi ,$ or about $3.14,$ radians.

A reflexive angle is an angle whose measure is greater than $180^{\circ }$ but less than $360^{\circ }.$ An alternative name for this type of angle is reflex angle. When using radians as the unit of measure, an angle is a reflexive angle when its measure is greater than $\pi ,$ or about $3.14,$ but less than $2\pi ,$ or about $6.28,$ radians.

A complete angle is an angle whose measure is exactly $360^{\circ }.$ Alternative names for this type of angle are full angle, round angle, and perigon. When using radians as the unit of measure, an angle is a complete angle when its measure is equal to $2\pi ,$ or about $6.28,$ radians.