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In the given figure, $O$ is the center of the circle and $ \angle AOB =120$

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How could I find the measure of $\angle AEB$?

Thanks in advance.

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    To be more specific about the ambiguity: if $AC$ and $BD$ were diameters (containing $O$), then $\angle AEB = \angle AOB = 120^{\circ}$. On the other hand, if $C$ and $D$ were to coincide (along the longer arc $AB$), then $E$ would coincide with them, so that $\angle AEB = \angle ACB = \angle ADB = 60^{\circ}$ (by the Inscribed Angle Theorem http://en.wikipedia.org/wiki/Inscribed_angle ). With $C$ and $D$ elsewhere, $\angle AEB$ is something else. This, even though the $\angle C$ and $\angle D$ --with $C$ and $D$ along the longer arc $AB$-- are *always* $60^{\circ}$ (by the IAT).2012-04-22

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As discussed in the comments, the measure of the angle depends on the positions of $C$ and $D$:

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