Looking at the image, the angles $\(x^{\circ}, y^{\circ}, z^{\circ}, v^{\circ}, u^{\circ}, t^{\circ}\)$ are angles around intersection lines.
From the arrangement:
- Around a point, the sum of angles is $\(360^{\circ}\)$.
- Vertical angles are equal.
- Adjacent angles on straight lines add up to $\(180^{\circ}\)$.

Let's analyze:
- The three angles in Column A are $\(x+z+u\)$.
- The three angles in Column B are $\(y+v+t\)$.

Because these angles are arranged around the intersecting lines, the sum of the angles on one side must equal the sum on the other side.

By vertical and linear pair angles properties, the two sums:

$$
\(x+z+u=y+v+t=180^{\circ}\)
$$

C is the answer