$\text{Angle}=\dfrac{\text{Arc length}}{\text{Radius}}$, a result or a definition? There is a commonly used formula to find an angle
$$
\text{Angle}=\dfrac{\text{Arc length}}{\text{Radius}}.
$$
My question is whether this is a deduced formula or it is the very definition of an angle? If this is the definition, why does this make sense? If this is formula, what is the proof?
Thanks!

It depends. You can define a radian as the angle subtended by om the centre of a circle which intercepts an arc equal in length to the radius of the circle. Or Equivalently you can say that total angle of one complete revolution is $ 2 \pi$.
In second case you can derive your formula from the definition, while in first it is a part of definition.
