What order must letters have to name an angle

The definition of angle is not clear and changes according to some authors. We usually call angle to the region of the plane limited by two half-lines having the same origin. We call the half-lines the side of the angle, while the origin is called the vertex of the angle.

We usually use 3 letters to represent an angle such as `ABC`. In this case, the letter that comes in the middle `B` always corresponds to the vertex; the first letter `A` corresponds to a point in the half-line that is the origin side, and finally comes the last letter `C` corresponding to a point of the half-line that is the extremity side. Finally, we also use a symbol in order not to have any doubt concerning the fact that we are talking about an angle: `/_ ABC`.

But, is it all the same to use `/_ABC` or `/_ CBA`?

Although both angles refer to the same region of the plane, they are different as it was previously explained in the scope of the origin side and the extremity side. Take notice of the following example:

The picture on the left refers itself to an angle with a positive amplitude, being called `/_ABC`, while the on your right refers to an angle having a negative amplitude, being called `/_CBA`. This kind of angle is known as a direction angle. When there are no doubts, or when orientation is not required, we can point out the angle just using the letter that represents the vertex. It is also useful to stress that when we want to point out the angle amplitude we must use a different symbol (a circumflex accent above the letter that represents the vertex). In this case we would have: `A hat B C = 60º`.

Check out our List of Questions to get to know a little more about the most diverse topics related to mathematics. If you have any pertinent (math) question whose answer can not easily be found, send us an email on the Contact page with the question. We will be happy to respond. In the event that you detect any errors in our answers, do not hesitate to contact us!