If BC bisects BED, this means that BED is split into two equal parts and that CED = BEC. We can see that AD forms a straight line, which means BED and AEB must be supplementary, ow have a sum of 180 degrees. Since CED has the same angle measure as BEC, this means that BED can be found by multiplying as shown:
[tex]BED = 2(CED) --> 2(4x + 1) --> BED = 8x + 2[/tex]
Now find the value of x:
[tex]11x - 12 + 8x + 2 = 180[/tex]
Combine like terms: [tex]11x + 8x - 12 + 2 = 180[/tex]
--> [tex]19x - 10 = 180[/tex]
---> [tex]19x - 10 + 10 = 180 + 10 --> 19x = 190[/tex]
Isolate x --> [tex]\frac{19x}{19} = \frac{190}{19}[/tex]
x = 10
Plug in the value of x:
[tex]AEB + BEC = ?[/tex]
--> [tex]11(10) - 12 + 4(10) + 1AEC[/tex]
---> [tex]110 - 12 + 40 + 1 = AEC[/tex]
----> [tex]98 + 41 = AEC[/tex]
So AEC is 139 degrees.
