Solve for x, y, w, and z in the given diagram. The angle indicated is 26 degrees.

The angle at the circumference is $26^\circ$. The central angle $x$ subtends the same arc (the arc from the top-left vertex to the bottom-right vertex). The angle subtended by an arc at the center is twice the angle subtended by the same arc at any point on the remaining part of the circle.

$$x = 2 \times 26^\circ$$ $$x = 52^\circ$$

Angles $x$ and $w$ are central angles that together form a full circle ($360^\circ$).

$$x + w = 360^\circ$$ $$52^\circ + w = 360^\circ$$ $$w = 360^\circ - 52^\circ$$ $$w = 308^\circ$$

The four vertices on the circle form a cyclic quadrilateral. In a cyclic quadrilateral, opposite angles sum to $180^\circ$. The angle $z$ is at the top-right vertex, and the angle $26^\circ$ is at the bottom-left vertex. These are opposite angles.

$$z + 26^\circ = 180^\circ$$ $$z = 180^\circ - 26^\circ$$ $$z = 154^\circ$$

The angle $y$ is at the top-left vertex. It subtends the arc from the bottom-left vertex to the top-right vertex. The central angle subtending this arc is not directly given. However, we can use the property that angles subtended by the same arc at the circumference are equal.
Alternatively, we can use the property that the angle at the circumference is half the central angle subtending the same arc.
Angle $y$ subtends the arc from the bottom-left vertex to the top-right vertex.
Angle $z$ subtends the arc from the bottom-left vertex to the bottom-right vertex.
Let's re-examine the diagram for $y$. Angle $y$ is at the top-left vertex. The angle opposite to $y$ in the cyclic quadrilateral is the angle at the bottom-right vertex. Let's call this angle $\alpha$. So $y + \alpha = 180^\circ$.
The angle $y$ subtends the arc from the bottom-left vertex to the top-right vertex.
The central angle $w$ is the reflex angle subtending the arc from the top-left vertex to the bottom-right vertex.
The angle $y$ is at the circumference and subtends the major arc from the bottom-left vertex to the top-right vertex.
The angle $z$ is at the circumference and subtends the major arc from the top-left vertex to the bottom-right vertex.
Let's use the property that angles subtended by the same arc at the circumference are equal.
Angle $y$ is at the top-left vertex. Angle $z$ is at the top-right vertex.
The angle $26^\circ$ is at the bottom-left vertex.
The central angle $x$ subtends the arc from the top-left vertex to the bottom-right vertex.
The angle $z$ is at the top-right vertex. It subtends the arc from the bottom-left vertex to the bottom-right vertex.
The central angle subtending the arc from the bottom-left vertex to the bottom-right vertex is not $x$ or $w$.

Let's re-evaluate $z$ and $y$ based on the central angles $x$ and $w$.
The angle $26^\circ$ is at the circumference and subtends the arc whose central angle is $x$. So $x = 2 \times 26^\circ = 52^\circ$.
The angle $z$ is at the circumference and subtends the arc whose central angle is $w$.

$$z = \frac{1}{2} w$$ $$z = \frac{1}{2} \times 308^\circ$$ $$z = 154^\circ$$

This matches the result from the cyclic quadrilateral property. This confirms the interpretation of $z$.

Now for $y$. Angle $y$ is at the circumference. It subtends the arc whose central angle is $x$.

$$y = \frac{1}{2} x$$ $$y = \frac{1}{2} \times 52^\circ$$ $$y = 26^\circ$$

Final values:
$z = \boxed{154^\circ}$
$y = \boxed{26^\circ}$
$w = \boxed{308^\circ}$
$x = \boxed{52^\circ}$