Triangle BEC is an isosceles triangle.
The angles opposite the congruent sides are equal
x = measure of missing angle
180 = 54 + 2x
Subtract 54 from both sides
126 = 2x
Divide both sides by 2
63 = x
angle EBC and angle C = 63 degrees
Angle EBC and angle EBA are supplementary.
This means they add up to 180 degrees
180 = 63 + EBA
Subtract 63 from both sides
117 = EBA
the measure of a triangle = 180
Therefore,
The measure of angle AEB = 180 - (40 + 117) = 23 degrees