Find the angle between two given lines 2D

Question

I am getting as an input 4 points.

p1=(x1, y1), p2=(x2, y2), p3=(x3, y3), p4=(x4, y4).

Now I have calculated the distances between p1p2, p2p3, p3p4 and p4p1.

Answer 1

Mathematically, the angle is acos(dot(||p2p1||, ||p2p3||)). Try

u21 = (p1 - p2) / norm(p1 - p2)
u23 = (p3 - p2) / norm(p3 - p2)
angle = acos(sum(u21 .* u23))

The prefix u indicates unit vectors.

Answer 2

To get the angle between two vectors, you simply use their inner product:

v1 = p1-p2;
v2 = p3-p2;

Normalize to unit vectors and take inner product:

n1 = v1/norm(v1);
n2 = v2/norm(v2);

cos_p2 = dot(n1,n2);

And the resulting angle is

acos(cos_p2)