Angles in a Quadrilateral Total 360°

Angles of a Quadrilateral

m∠DAB = 78.69°

m∠ABC = 86.633°

m∠BCD = 123.111°

m∠CDA = 71.565°

m∠DAB + m∠ABC + m∠BCD + m∠CDA = 360.00°

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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

B

D

. (The other diagonal

A

C

could be used instead.) Then the angle

A

B

C

(and

C

D

A

) overlaps itself and the common part is counted twice.