In a circle with center O, chords AB and CD intersect at point E. If CDA = 36^ and CAD = 54^, find COD.

Since $O$ is the center and $OC = OD$ (radii), $\triangle OCD$ is an isosceles triangle.
Given $\angle CDA = 36^\circ$, which is $\angle ODC$.
Therefore, $\angle OCD = \angle ODC = 36^\circ$.
The sum of angles in $\triangle OCD$ is $180^\circ$.

$$\angle COD = 180^\circ - (\angle OCD + \angle ODC) = 180^\circ - (36^\circ + 36^\circ) = 180^\circ - 72^\circ = 108^\circ$$