# how to find concave angle between three points

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Eliska Paulikova on 22 Nov 2022
Answered: David Goodmanson on 23 Nov 2022
Hello how can I fing agle if I know three points, but I would like to reald also the concave one.
this function ang = atan2(norm(det([P2-P0;P1-P0])),dot(P2-P0,P1-P0)); , it gives me only convex one
thank you
Eliska Paulikova on 22 Nov 2022
Thank you so much
It means a lot for me
thank you

David Goodmanson on 23 Nov 2022
Hi Eliska,
One thing that does not seem to be mentioned so far is your use of the norm function on the determinant. That makes all the sines positive, which puts you into the first or second quadrant and forces all the angles out of atan2d to be 0<=theta<180. Dropping the norm opens up the range of angles to 0<=theta<360. In the code below, (P2-P0) is a reference vector, and the angle is measured counterclockwise from (P2-P0) to (P1-P0) with 0<=theta<360.
P0 = [0 0];
P1 = [-1 2];
P2 = [1 1];
P20 = P2-P0; % reference vector
P10 = P1-P0;
theta = atan2d((det([P20;P10])),dot(P20,P10));
theta = mod(theta,360)

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