To classify each angle in the given figure as an inscribed angle or a central angle, let's first understand the definitions:

1. Inscribed Angle: An angle formed by two chords in a circle which have a common endpoint.
2. Central Angle: An angle whose vertex is at the center of the circle and whose sides are radii of the circle.

Given the circle with points $R, S, T, U, V, W, X$, let's classify each angle:

1. $\angle XWR$:

   • This angle has $W$ as the vertex and points $X$ and $R$ on the circumference. Since $W$ is not the center, $\angle XWR$ is an inscribed angle.

2. $\angle VST$:

   • This angle has $S$ as the vertex and points $V$ and $T$ on the circumference. Since $S$ is not the center, $\angle VST$ is an inscribed angle.

3. $\angle VWU$:

   • This angle has $W$ as the vertex and points $V$ and $U$ on the circumference. Since $W$ is not the center, $\angle VWU$ is an inscribed angle.

4. $\angle XRU$:

   • This angle has $R$ as the vertex and points $X$ and $U$ on the circumference. Since $R$ is not the center, $\angle XRU$ is an inscribed angle.

Now, let's fill in the table based on the above analysis:

Do you want more details or have any questions?

Here are some related questions to further your understanding:

1. What is the difference between a chord and a radius in a circle?
2. How can you find the measure of an inscribed angle given the measure of its intercepted arc?
3. How do central angles relate to the arcs they intercept?
4. Can an inscribed angle ever be a right angle? If so, under what conditions?
5. What is the relationship between the measure of a central angle and the measure of its corresponding inscribed angle?

Tip: Remember that an inscribed angle is always half the measure of the central angle that intercepts the same arc.