Respuesta :

tramserran

∠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°


MrRoyal

An angle bisector divides an angle into two equal halves. The measure of angle AEC is: [tex]139^o[/tex]

Given that:

[tex]\angle AEB = 11x - 12[/tex]

[tex]\angle CED = 4x + 1[/tex]

Since ray BD bisects [tex]\angle BED[/tex], then:

[tex]\angle BEC = \angle CED[/tex]

This implies that:

[tex]\angle BEC = 4x + 1[/tex]

[tex]\angle AEC[/tex] is calculated as:

[tex]\angle AEC = \angle AEB + \angle BEC[/tex]

This gives:

[tex]\angle AEC = 11x - 12 + 4x + 1[/tex]

Collect like terms

[tex]\angle AEC = 11x + 4x- 12 + 1[/tex]

[tex]\angle AEC = 15x-11[/tex]

Next, we calculate the value of x as follows:

[tex]\angle AEB + \angle CED + \angle BEC = 180[/tex] --- angle on a straight line.

This gives:

[tex]11x - 12 + 4x + 1 + 4x + 1 = 180[/tex]

Collect like terms

[tex]11x + 4x + 4x = 180+12-1-1[/tex]

[tex]19x = 190[/tex]

Divide by 19

[tex]x = 10[/tex]

Substitute 10 for x in [tex]\angle AEC = 15x-11[/tex]

[tex]\angle AEC= 15 \times 10 - 11[/tex]

[tex]\angle AEC= 139^o[/tex]

Hence, the measure of [tex]\angle AEC[/tex] is [tex]139^o[/tex]

Read more about angle bisector at:

brainly.com/question/12896755