  We study N=1 supersymmetric four-dimensional solutions of massive Type IIA
supergravity with intersecting D6-branes in the presence NS-NS three-form
fluxes. We derive N=1 supersymmetry conditions for the D6-brane and flux
configurations in an internal manifold $X_6$ and derive the intrinsic torsion
(or SU(3)-structure) related to the fluxes. In the absence of fluxes, N=1
supersymmetry implies that D6-branes wrap supersymmetric three-cycles of $X_6$
that intersect at angles of SU(3) rotations and the geometry is deformed by
SU(3)-structures. The presence of fluxes breaks the SU(3) structures to SU(2)
and the D6-branes intersect at angles of SU(2) rotations; non-zero mass
parameter corresponds to D8-branes which are orthogonal to the common cycle of
all D6-branes. The anomaly inflow indicates that the gauge theory on
intersecting (massive) D6-branes is not chiral.
