a) ∠PQR=65° (alternate interior angles theorem)
∠PRQ = 60° (linear pair)
x = 55° (angles in a triangle add to 180°)
b) ∠APQ and ∠PQR are congruent alternate interior angles.
This question seems to me to be an exercise in applying the rule for a difference of squares in order to rewrite the difference of two relatively large numbers as the "simpler" product of other integers.
The lcm of 1978 and 2832 is
2800848