What is the static view of angle?

As well as the idea of an angle as a rotation there is also the static view of angle. This is where we focus our attention on how pointed is the shape formed by the two lines. But the angle is still a measurement: we can think of it as a measurement of the difference in direction between the two lines. So, for example, in the diagram shown on the right the angle marked in (a) is greater than that marked in (b). This is because the two lines in (b) are pointing in nearly the same direction, whereas the difference in the direction of the two lines in (a) is much greater.

Thinking of angle as the difference in direction between two lines helps to link the static view of angle with the dynamic one of rotation, because the obvious way to measure the difference in two directions is to turn from one to the other and measure the amount of turn.