2. Use three regular polygon tiles with equal side lengths to pave the ground, with their vertices fitting together, just enough to completely cover the ground. Given the number of sides of the regular polygons are $x, y, z$. Then the value of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ is $(\quad)$.
(A) 1
(B) $\frac{2}{3}$
(C) $\frac{1}{2}$
(D) $\frac{1}{3}$
2. C.

According to the problem, we have
$$
\begin{array}{l}
\frac{x-2}{x} \times 180^{\circ}+\frac{y-2}{y} \times 180^{\circ}+\frac{z-2}{z} \times 180^{\circ}=360^{\circ} \\
\Rightarrow \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{2} .
\end{array}
$$