ABCD is a cyclic quadrilateral in which $$\angle$$A = $$67^\circ$$ and $$\angle$$B = $$92^\circ$$. What is the difference between the measures of $$\angle$$C and $$\angle$$D?

As per the given question,

ABCD is a cyclic quadrilateral.

$$\angle A=67^\circ$$ and $$\angle B=92^\circ$$

But we know that the sum of opposite angle of the cyclic quadrilateral$$= 180$$

So, $$\angle B+\angle D=180^\circ$$----------(i)

and $$\angle C+\angle A=180^\circ$$-----------(ii)

Now from the equation (i) and equation (ii),

$$\Rightarrow \angle C- \angle D \angle A-\angle B=0$$

$$\Rightarrow \angle C- \angle D +67^\circ-92^\circ=0$$

$$\Rightarrow \angle C- \angle D=25^\circ$$