ABCD is a cyclic quadrilateral. Angle ADC = 64 degrees. Find angle ABC (z).

Let's find the values of w, x, y, and z.

The diagram shows a cyclic quadrilateral ABCD, meaning all its vertices lie on the circle. There is also a smaller inner circle with its center, which we'll call P.

Step 1: Find z.
ABCD is a cyclic quadrilateral. In a cyclic quadrilateral, opposite angles sum to $180^\circ$.
We are given $\angle ADC = 64^\circ$. Angle z is $\angle ABC$.

$$\angle ABC + \angle ADC = 180^\circ$$ $$z + 64^\circ = 180^\circ$$ $$z = 180^\circ - 64^\circ$$ $$$$