Angle-6 is congruent to Angle-3.
They are "alternate interior angles" formed by a transversal cutting across parallel lines. These are always congruent, according to a widely studied theorem of 9th grade plane geometry.
Angle-2 is also congruent to Angle-3, because they are a pair of "vertical angles".
And, since Angle-6 is congruent to Angle-3, Angle-7 is too, because it forms a pair of vertical angles with Angle-6.
These don't depend on parallel lines, only on 'vertical angles'.
