8. Let $I$ be the incenter of $\triangle A B C$, and $3 \overrightarrow{I A}+4 \overrightarrow{I B}+5 \overrightarrow{I C}=\mathbf{0}$. Then the size of angle $C$ is $\qquad$
Consider $\triangle A B C$ with the inradius $r$, note that $I A=\frac{r}{\sin \frac{A}{2}}, I B=\frac{r}{\sin \frac{B}{2}}, I C=\frac{r}{\sin \frac{C}{2}}$,
$$
\begin{array}{l}
\Rightarrow\left\{\begin{array} { l } 
{ 3 y z = x ( 4 z ^ { 2 } + 5 y ^ { 2 } ) , } \\
{ 4 x z = y ( 4 z ^ { 2 } + 5 x ^ { 2 } ) , } \\
{ 5 x y = z ( 3 y ^ { 2 } + 4 x ^ { 2 } ) }
\end{array} \Rightarrow \left\{\begin{array} { l } 
{ 3 x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1 , } \\
{ 2 y ^ { 2 } + x ^ { 2 } + z ^ { 2 } = 1 , } \\
{ 7 z ^ { 2 } + 5 x ^ { 2 } + 5 y ^ { 2 } = 5 }
\end{array} \Rightarrow \left\{\begin{array}{l}
x^{2}=\frac{1}{10}, \\
y^{2}=\frac{1}{5}, \\
z^{2}=\frac{1}{2}
\end{array} \Rightarrow C=90^{\circ} .\right.\right.\right. \\
\end{array}
$$