Let ABCD be a quadrilateral, such that  = 96°; B̅ = 132°. The bisector of angle C and D meet at point E. Find the measure of angle CED

To find the measure of angle \( CED \) where the angle bisectors of angles \( C \) and \( D \) meet, we need to first determine the measures of angles \( C \) and \( D \).

In a quadrilateral, the sum of the interior angles is \( 360^\circ \). Therefore, we can calculate angle \( C \) and angle \( D \) using the measures of angles \( A \) and \( B \):

\[
\angle A + \angle B + \angle C + \angle D = 360^\circ
\]

Substituting the known values:

\[
96^\circ + 132^\circ + \angle C + \angle D = 360^\circ
\]

Calculating the sum of \( A \) and \( B \):

\[
96^\circ + 132^\circ = 228^\circ
\]

Now, we can find the sum of angles \( C \) and \( D \):

\[
\angle C + \angle D = 360^\circ - 228^\circ = 132^\circ
\]

Let \( \angle C = x \) and \( \angle D = 132^\circ - x \).

Next, since \( E \) is the intersection of the angle bisectors, the angle at \( E \) can be expressed as:

\[
\angle CED = \frac{1}{2}(\angle C + \angle D)
\]

Thus,

\[
\angle CED = \frac{1}{2}(x + (132^\circ - x)) = \frac{1}{2}(132^\circ) = 66^\circ
\]

Therefore, the measure of angle \( CED \) is:

\[
\boxed{66^\circ}
\]