Wolfram Demonstrations Project

The sum of the angles in a quadrilateral is 360° regardless of the positions of the vertices.

When the quadrilateral crosses itself, think of it of as being folded over the diagonal

. (The other diagonal

could be used instead.) Then the angle

(and

) overlaps itself and the common part is counted twice.

Contributed by: Abby Brown

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Common Core State Standards for Mathematics

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Angles in a Quadrilateral Total 360°