Question

PLEASE HELP ME!!! Please help me find the measure of AEC, and please show all work. Thanks :)))

Answer 1

Given: ∠AEB = 11x - 12, ∠CED = 4x + 1, Line EC bisects ∠BED

To find: ∠AEC

Since Line EC bisects ∠BED, ∠BEC = ∠CED

That is: ∠BEC = 4x + 1

Therefore ∠BEC + ∠CED = 4x + 1 + 4x + 1 = 8x + 2

Now, ∠AEB = 11x - 12

Therefore: ∠AEB + ∠BEC = ∠AEC

That is, 11x - 12 + 4x + 1 = ∠AEC

∠AEC = 15x - 11

Therefore ∠AEC = 15x - 11

Hopeit helps :)

Answer 2

∠BEC ≅ ∠CED          definition of angle bisector

∠BEC = ∠CED           definition of congruency

∠AEB , ∠BEC, and ∠CED are supplementary    

∠AEB + ∠BEC + ∠CED = 180    definition of supplementary angles

∠AEB + ∠CED + ∠CED = 180    substitution

11x - 12 + 4x + 1 + 4x + 1 = 180    substitution

19x - 10 = 180              simplified (added like terms)

19x = 190                    addition property of equality

  x = 10                       division property of equality

*****************************************************************

∠AEB = 11x - 12

         = 11(10) - 12

          = 110 - 12

          = 98

∠BEC = ∠CED = 4x + 1

                        = 4(10) + 1

                         = 40 + 1

                          = 41

********************************************************************

∠AEB + ∠BEC = ∠AEC   segment addition property

98 + 41 = ∠AEC               substitution

 139 = ∠AEC                  simplified (added like terms)

Answer: 139°