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6) AEB + BEC + DEC = 180

     70   + BEC + 30   = 180

                BEC + 100 = 180

                          BEC = 80°

7) ∠2 ≅ ∠4   because they are vertical angles

   ∠2 = ∠4    definition of congruency

   88° = ∠4   substitution

8) complement means their sum equals 90°

    20° + x = 90°

            x = 70°

9) AEB + BED = 180    because they are a linear pair

   AEB +  120  = 180

              AEB = 60°

10) ∠2 + ∠3 = 180      because they are a linear pair

5x + 10 + x + 50 = 180   substitution

            6x + 60 = 180   simplify (add like terms)

                     6x = 120   subtraction property of equality

                       x = 20   division property of equality

11) ∠1 ≅ ∠3    because they are vertical angles

   ∠1 = ∠3     definition of congruency

3x - 40 = x + 10   substitution

2x - 40 = 10        subtraction property of equality

      2x = 50       addition property of equality

        x = 25       division property of equality

12) AEB + CEB + CED = 180     supplementary angles

       4x  +   9x  +   2x  = 180     substitution

                            15x = 180      simplify (add like terms)

                               x = 12         division property of equality

CED = 2x   = 2(12)   = 24°

13) complement means their sum equals 90°

   x + complement = 90°

         complement = 90° - x

14) supplement means their sum equals 180°

5x + 30° + supplement = 180°

         5x + supplement = 150°

                supplement = (150 - 5x)°

15) x + 8x = 180

           9x = 180

             x = 20

8x    = 8(20)   = 160°

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