In the figure, the bisectors of $\angle B$ and $\angle C$ meet at $I$.
If $\angle A=70^{\circ}$ and $\angle B I C=x^{\circ}$, find $x$.
G6.2 A convex $n$-sided polygon has 35 diagonals. Find $n$.
G6.3 If $y=a b-a+b-1$ and $a=49, b=21$, find $y$.
G6.4 If $K=1+2-3-4+5+6-7-8+\ldots+1001+1002$, find $K$.
$\begin{array}{l}\text { Let } \angle A B I=b=\angle C B I, \angle A C I=c=\angle B C I \\ 2 b+2 c+70=180(\angle \mathrm{s} \text { sum of } \triangle) \\ b+c=55 \\ \text { In } \triangle B C I, b+c+x=180(\angle \mathrm{s} \text { sum of } \Delta) \\ x=180-55=125 \\ C_{2}^{n}-n=35 \\ \Rightarrow \frac{n(n-3)}{2}=35 \\ n^{2}-3 n-70=0 \\ \Rightarrow(n-10)(n+7)=0 \\ n=10 \\ y=(a+1)(b-1)=(49+1)(21-1)=50 \times 20=1000 \\ K=1+(2-3-4+5)+(6-7-8+9)+\ldots+(998-999-1000+1001)+1002=1003 \\\end{array}$