Two triangles
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You can put 2 triangles in a square or you can call it a quadrilateral.
No matter what, any Euclidean quadrilateral can be composed of 2 triangles, thus, giving the quadrilateral 360o (because triangles contain an angle value of 180o). Also, since a quadrilateral contains 4 sides, it is possible for a triangle to intercept on the 2 sides, and produce a 4 sided figure.
it's impossible to have a quadrilateral that can't be cut into triangles.
4
Any quadrilateral such as a 4 sided trapezium can be divided into 2 triangles