My teacher defined an angle as the measure of the size of rotation of a ray around the vertex. But recently I stumbled across the Wikipedia article on angles, which defines an angle as the figure formed by two rays with a common endpoint, the vertex. So which definition is correct? Are both of them correct, perhaps?
Also, how exactly should I visualize this "figure"? The Wikipedia article provides the following picture:
So is that green sector the angle? Or is it both of the rays combined? I'm really confused and would appreciate any help