what i get is:
yes, the slata going in the same direction are parallel to each other.
angle A is a vertical angle with a 50 degree angle, therefore it is also 50 degrees.
angle B is part of parallelogram PQRS (my nomenclature) and is adjacent angle to angle PQR which is 80 degrees because it is a vertical angle with the 80 degree angle shown.
since angle PQR is adjacent to angle PQR, then it is supplementary to it and is therefore 100 degrees.
angle PQR is the angle B that was given in the original diagram.
angle PSR is part of parallelogram PQRS and is opposite the 80 degree angle PQR and is therefore 80 degrees as well because opposite angles of a parallelogram are congruent.
angle C is vertical to angle PSR and is therefore also 80 degrees.
my answers:
angle A is 50 degrees.
angle B is 100 degrees.
angle C is 80 degrees.
here's my diagram of the diagram you were given.
in this diagram:
lines x, y, and z are all horitonztal lines and therefore parallel to each other.
lines DG and EF are parallel to each other since they are on oppositie sides of the slat.
lines HK and IJ are paralell to each other since they are on opposite sides of the same slat.
PQRS is a parallelogram because opposite sides of it are parallel to each other.
angle PQR is 80 degrees because it is vertical angle to the 80 degree angle shown.
angle PSR is also 80 degrees because opposite angles of a parallelogram are congruent.
angle SPQ is 100 degrees because it is an adjacent angle to the 80 degree angles of the parallelogram and adjacent angles of a parallelogram are supplementary.
angle SRQ is also 100 degrees because it is opposite to angle SPQ and opposite angles of a parallelogram are congruent.
angle C is 80 degrees because it is a vertical angle to angle PSR which is 80 degrees.
that should be it.
there are other relationships formed from the diagram but they are unnecessary to provide you with the answer you seek.