# Is a single line, line segment, or ray a valid angle?

After online research and several definitions of the term angle it seems they all fit a short set of restrictions for what defines an angle, "a shape formed by two rays that intersect at a point called the vertex."

Given this definition a ray or line segment on its own is not an angle because it would require at least two of either to form the shape. So how then is an angle of zero degrees a valid angle? Is it not the exact same as a line segment or ray?

Is an angle of zero degrees not actually an angle or is it for some reason an exception to the rule?

• A 0º angle is made up of two lines, directly on top of each other. Therefore the angle, or the space between them is 0º. – Toby Mak Jul 3 '18 at 4:02

$$\theta = \arccos\left(\dfrac{\vec u\cdot \vec v}{||\vec u|| *||\vec v||}\right)$$
And if $\vec u = \vec v$ then you get
$$\theta = \arccos \left(1\right) = 0$$