Why concave quadrilateral do not have 360 degree as sum of all angles.

A special case of crossed quadrilaterals are the antiparallelograms, crossed quadrilaterals in which (like a parallelogram) each pair of nonadjacent sides has equal length. The diagonals of a crossed or concave quadrilateral do not intersect inside the shape and one angle is refler angle.

 

If you cut any quadrilateral along one of its diagonals, the figures formed are two triangles. Since the sum of the angles of a triangle is 180 degrees, then the sum of the angles of two triangles is 2(180) = 360 degrees. For this reason, the sum of the angles of a quadrilateral is 360 degrees.