Hey there!!
We know:
Angle CED = 4x+1
And the line EC bisects the angle BED.
What does bisect mean?
Bisecting is something which cuts something into half.
Hence,
Angle BEC would also be 4x+1
Angle AEB = 11x-12
Now, we know that the total angle is 180°
Hence,
... 4x+1+4x+1+11x-12 = 180
Combining like terms:
... 8x+2+11x-12 = 180
... 19x-10 = 180
Adding 10 on both sides:
... 19x= 180+10
... 19x=190
Dividing 19 on both sides:
... x = 190/19
... x = 19.
Angle AEB+BEC=?
... 11x-12+4x+1=?
... 11(19)-12+4(19)+1=?
... 209-12+76+1=?
... 274.
Hence, the required answer is 274°.
Hope my answer helps!!
