It is given that ∠XYZ = 64° and XY is produced to point P. A ray YQ bisects ∠ZYP. Draw a figure from the given information. Find ∠XYQ and reflex ∠QYP.

Let us draw a figure from the given,

Given that, a ray YQ bisects ∠ZYP

So, ∠QYP = ∠ZYQ

Here, PX is a straight line, so the sum of the angles is equal to 180°

∠XYZ + ∠ZYQ + ∠QYP = 180°

Given that, ∠XYZ = 64° and ∠QYP = ∠ZYQ

⇒ 64° + 2∠QYP = 180°

⇒ 2∠QYP = 180°-64° = 116°

∴ ∠QYP = = 58°

Also, ∠QYP = ∠ZYQ = 58°

Using the angle of reflection,

∠QYP = 360°-58° = 302°

∠XYQ = ∠XYZ + ∠ZYQ

⇒∠XYQ = 64° + 58° = 122°

∴ Reflex ∠QYP = 302° and ∠XYQ = 122°