Points A, D, C, B and E are concyclic. If $$\angle$$AEC = 50$$^\circ$$ and $$\angle$$ABD = 30$$^\circ$$, then what is the measure(in degrees) of  $$\angle$$CBD?

ADCE is a cyclic quadrilateral, so opposite angles are supplementary.

$$\Rightarrow$$  $$\angle$$ADC + $$\angle$$AEC = 180$$^\circ$$

$$\Rightarrow$$  $$\angle$$ADC + 50$$^\circ$$ = 180$$^\circ$$

$$\Rightarrow$$  $$\angle$$ADC = 130$$^\circ$$

ABCD is a cyclic quadrilateral, so opposite angles are supplementary.

$$\Rightarrow$$ $$\angle$$ABC + $$\angle$$ADC = 180$$^\circ$$

$$\Rightarrow$$ x + 30$$^\circ$$ + 130$$^\circ$$ = 180$$^\circ$$

$$\Rightarrow$$ x = 20$$^\circ$$

$$\Rightarrow$$  $$\angle$$CBD = x = 20$$^\circ$$

Hence, the correct answer is Option A