Directed Angles and Their Types

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Angles can be defined as an ordered pair of rays that meet at a vertex.


The definition is ambiguous as soon as the measure of angle is introduced. Suppose the angle is formed by the positive axis and the positive axis. Is the measure of the angle 90° or 270°?

A small arc going from one ray to the other shows which one is meant.

If the small arc has an arrow, the angle is directed. Switching the arrow gives the negative of the angle and changes the sign of its measure.


Contributed by: George Beck (July 2018)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.