Answer:Angle AEC is 139 degrees.
Step-by-step explanation:
Since line EC bisects angle BED, it divides angle BED equally into 2. This means that
Angle BEC = angle CED
If angle CED = 4x + 1
Therefore,
Angle BED = 2 × angle CED
= 2(4x + 1) = 8x + 2
The sum of the angles in a straight line is 180 degrees. Therefore
Angle AEB + angle BED = 180
Angle AEB = 11x - 12. Therefore
11x - 12 + 8x + 2 = 180
19x - 10 = 180
19x = 180 + 10 = 190
x = 190/19 = 10
Angle BEC = 4x + 1 = 4×10 + 1 = 41
Angle AEB = 11x - 12 = 11×10 - 12 = 98
Angle AEC = 41 + 98 = 139
