Generally speaking, the angle between two lines is defined as the angle that the one of them must be rotated in order to match the slope of the other one.
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If we have two intersecting non-vertical lines, the angle between them is: β = φ+α ⇒ φ = β-α Therefore, tan(φ) = tan(β-α) = (tan(β)-tan(α))/(1+tan(β)tan(α)). So if your lines are y = a1x+b1 and y = a2x+b2 the angle between them is tan(φ) = (a1- a2)/(1+a1a2) If one of the lines is vertical, the angle between it and y = ax+b is tan(φ) = 1/a |
| Form | Angle between the lines |
y = a1x+b1 |
φ =arctan (a1- a2)/(1+a1a2) |
| y = y01t + yf1 x = x01t + xf1 y = y02t + yf2 x = x02t + xf2 |
or
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Four points: (x1,y1) , (x2,y2) |
 Gives the angle that the SECOND (x3,y3) ,(x4,y4) line must be rotated counter-clockwise in order to match the FIRST line (x1,y1) , (x2,y2) |
a1x+b1y+c1 = 0 and |
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