Me find the measure of aec, and show all work. :

An angle bisector divides an angle into two equal halves. The measure of angle AEC is:

Given that:

Since ray BD bisects , then:

This implies that:

is calculated as:

This gives:

Collect like terms

Next, we calculate the value of x as follows:

--- angle on a straight line.

This gives:

Collect like terms

Divide by 19

Substitute 10 for x in

Hence, the measure of is

Read more about angle bisector at:

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∠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)

139°

answer: ok

step-by-step explanation: