# Calculate angles between two intersecting lines using the slopes

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hu on 14 Aug 2014
Commented: Amit Haldar on 6 Jan 2016
Hi,
I have two slopes M1 and M2 that I wish to check the angle between them.
I was told that I can use the inverse tangent of (m1 - m2)/(1 + m1*m2)
atand((m1-m2)/(1-m1*m2))
Is it true, why? What is the difference if I use the (m1 - m2)/(1 - m1*m2) instead?
Thanks
Amit Haldar on 6 Jan 2016
Yes that is how we calculate the angle between two lines.

Roger Stafford on 14 Aug 2014
That formula comes from the trigonometric identity
tan(A-B) = (tan(A)-tan(B))/(1+tan(A)*tan(B))
Note: You have the sign wrong in atand((m1-m2)/(1-m1*m2))
It should be understood that taking the arctangent (atand) of your expression corresponds to rotating the line with slope m2 in both a counterclockwise and a clockwise direction around the intersection point until first encountering the line with slope m1. Going counterclockwise counts as a positive angle and clockwise is considered negative. Therefore your answer will lie between +90 and -90.
hu on 15 Aug 2014
yep

Rick Rosson on 14 Aug 2014
phi = atan(m1) - atan(m2);

Amir on 14 Aug 2014
This image is from this video: https://www.youtube.com/watch?v=4bGt5wQf818
Hope this can clarify this for you.