1. The problem asks to find the values of $x$, $y$, and $z$ given some angles: $40^\circ$, $121^\circ$, and others labeled $A$, $B$, $C$, $D$, $z^\circ$, $x^\circ$, $y^\circ$. 2. Since the problem does not provide explicit equations or relationships, we assume these angles are part of a geometric figure, likely a triangle or polygon, where the sum of interior angles is known. 3. For a triangle, the sum of interior angles is always $$180^\circ$$. 4. If $x$, $y$, and $z$ are angles in a triangle, then: $$x + y + z = 180^\circ$$ 5. Given one angle is $40^\circ$ and another is $121^\circ$, if these correspond to $x$ and $y$, then: $$x = 40^\circ, \quad y = 121^\circ$$ 6. Substitute into the sum equation: $$40^\circ + 121^\circ + z = 180^\circ$$ 7. Simplify: $$161^\circ + z = 180^\circ$$ 8. Solve for $z$: $$z = 180^\circ - 161^\circ = 19^\circ$$ 9. Therefore, the values are: $$x = 40^\circ, \quad y = 121^\circ, \quad z = 19^\circ$$