It is given that ∠ XYZ = 64° and XY is produced to point P.

∠PYZ + ∠XYZ = 180° [∵ Linear Pair]
⇒ ∠PYZ + 64° = 180° [∵ ∠XYZ = 64°]
⇒ ∠PYZ = 180° – 64° = 116°
But,
∠PYQ = ∠ZYQ = 1/2 ∠PYZ [∵ ∠ZYP is bisected by ray YQ]
∴ ∠PYQ = ∠ZYQ = 1/2 × 116° = 58°
∴ ∠XYQ = ∠XYZ + ∠ZYQ = 64° + 58° = 122 and
Reflex ∠QYP = 360° – ∠QYP = 360° – 58° = 302°