In the given figure, if $AD=CD=BC$, then the $∠CDB$ is:

64°

We are given that :-

In triangle ADC

AD = DC  ( Given )

So,  ∠DAC = ∠DCA   [Angles opposite to equal sides are equal]

Let us consider that , ∠DAC = ∠DCA = x             

 So, By using  exterior angle property ,

∠CDB = 2θ        

In triangle CDB

CD = CB   ( Given )

 ∠CDB = ∠CBD = 2x  [Angles opposite to equal sides are equal]  

Now, In triangle ABC

 [By Using exterior angle property]

 96° = ∠ CAB + ∠ CBA  

 96° = x + 2x

 x = 32°

Now,

∠CDB = 2x

= 2 x 32°

= 64°