How to calculate the reflex angles of a polygon in the 1st quadrant ?

I have a complex polygon in the 1st quadrant. I have all the vertices. I want to measure its internal angles. Some of them are reflex angles. when I use

internal(k) = atan2( abs((x2-x1)*(y3-y1)-(y2-y1)*(x3-x1)),(x2-x1)*(x3-x1)+(y2-y1)*(y3-y1) ) * 180/pi;

it is finding only the angles < pi.

How do I get the reflex angles also (all x and y signs are +ve) ?

Thanks

Answer 1

[Matt J]

I don't know how you arrived at your formula, but using abs() in the first argument to atan2 ensures that the result must be between 0 and pi.

atan2(Y,X) must be in [0,pi] whenever Y>=0.