Question

the opposite angles of a parallelogram are congruent

Answer 1

yes the opposite angle of a parallelogram are congruent according to the properties.
if you want to prove it than use the diagnol property.

Answer 2

Given:
ABCD is a parallelogram

To prove:
∠A = ∠C and ∠B = ∠D

Proof:
AB||CD (ABCD is a ||gm) and AC is the transversal

Hence, ∠1 = ∠4 (Alternate Interior angles) -(1)

→ ΔABC ≅ ΔADC (Diagnols of ||gm divide it into two congruent Δs)

Hence ,∠3 = ∠4 → (2) [CPCT]
and ∠1 = ∠2 → (3)

∠A = ∠3 + ∠4
∠A= ∠4 + ∠4 [From (2)]
∠A= 2∠4 = 2∠1 [From (1)]
∠A= ∠1 + ∠2
∠A = ∠C

Therefore, ∠A = ∠C.
Similarly, ∠B = ∠D. [PROVED]