How to calculate an angle from three points?

If you mean the angle that P1 is the vertex of then using the Law of Cosines should work:

arccos((P₁₂² + P₁₃² - P₂₃²) / (2 * P₁₂ * P₁₃))

where P₁₂ is the length of the segment from P1 to P2, calculated by

sqrt((P1_x - P2_x)² + (P1_y - P2_y)²)

It gets very simple if you think it as two vectors, one from point P1 to P2 and one from P1 to P3

so:
a = (p1.x - p2.x, p1.y - p2.y)
b = (p1.x - p3.x, p1.y - p3.y)

You can then invert the dot product formula:

to get the angle:

Remember that just means: a1*b1 + a2*b2 (just 2 dimensions here...)