6. As shown in Figure 2, fold the hexagon $A B C D E F$ along the line $G H$ so that points $A$ and $B$ fall inside the hexagon $C D E F G H$. Let $\angle C+\angle D+\angle E+\angle F = \alpha$. Then which of the following conclusions must be true? ( ).
(A) $\angle 1+\angle 2=900^{\circ}-2 \alpha$
(B) $\angle 1+\angle 2=1080^{\circ}-2 \alpha$
(C) $\angle 1+\angle 2=720^{\circ}-\alpha$
(D) $\angle 1+\angle 2=360^{\circ}-\frac{1}{2} \alpha$
6.B.

As shown in Figure 9, let the extension of FA intersect the extension of CB at point P, and the extension of GA' intersect the extension of HB' at point P'.
By symmetry, we know
$$
\begin{array}{c}
\angle 1=2 \angle A P P^{\prime}, \\
\angle 2=2 \angle B P P^{\prime}. \\
\text { Then } \angle 1+\angle 2=2 \angle A P B. \\
\text { Also, } \angle A P B=540^{\circ}-\alpha, \text { so } \\
\angle 1+\angle 2=1080^{\circ}-2 \alpha \text {. }
\end{array}
$$