From figure,

∠XYZ = 64° (Given)

Now, ∠ZYP + ∠XYZ = 180°

(Linear pair axiom) ⇒

∠ZYP + 64° = 180°

⇒ ∠ZYP = 180° – 64° – 116°

Also, given that ray YQ bisects ∠ZYP.

But, ∠ZYP = ∠QYP ∠QYZ = 116°

Therefore, ∠QYP = 58° and ∠QYZ = 58°

Also, ∠XYQ = ∠XYZ + ∠QYZ

⇒ ∠XYQ = 64° + 58° = 122°

and reflex ∠QYP = 360° – ∠QYP = 360° – 58° = 302° (∵ ∠QYP = 58°)

Hence, **∠XYQ = 122° and reflex ∠QYP = 302° Ans.**