Since,

l₁‖ l₂

And PQ cuts them

∠DPQ + ∠PQE = 180^o (Consecutive interior angles)

a + a + b + b = 180^o

2 (a + b) = 180^o

a + b = 90^o (i)

In

∠PAQ + a + b = 180^o

∠PAQ = 90^o

∠PAQ + x + x = 180^o (Linear pair)

90^o + 2x = 180^o

x = 45^o