The sum of the measures of the angles of a convex quadrilateral is 360 degrees.

1.     Convex Quadrilateral ABCD.                         1.        Given.

2.     Draw diagonal BD.                                           2.        Definition of diagonal.

3.     /  ABD + /  BDA + /  DAB = 180.                     3.        Triangle Sum Theorem.

4.     /  BCD + /  CDB + /  DBC = 180.                     4.        Triangle Sum Theorem.

5.     /  ABD + /  BDA + /  DAB +                             5.        Addition Property.

        /  BCD + /  CDB + /  DBC = 360.

6.     /  ABC = /  ABD + /  DBC.                                6.        Angle Addition.

7.     /  CDA = /  BDA + /  CDB.                                7.        Angle Addition.

8.     /  DAB + /  ABC + /  BCD + /  CDA = 360.       8.        Substitution.

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