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

Given, ∠XYZ = 64°
∠YQ bisects ∠ZYP
∠XYZ + ∠ZYP = 180° (Linear Pair)
⇒ 64° + ∠ZYP = 180°
⇒ ∠ZYP = 116°
Also, ∠ZYP = ∠ZYQ + ∠QYP
∠ZYQ = ∠QYP (YQ bisects ∠ZYP)
⇒ ∠ZYP = 2∠ZYQ
⇒ 2∠ZYQ = 116°
⇒ ∠ZYQ = 58° = ∠QYP
Now, ∠XYQ = ∠XYZ + ∠ZYQ
⇒ ∠XYQ = 64° + 58°
⇒ ∠XYQ = 122°
Also, reflex ∠QYP = 360° - ∠QYP = 360° - 58° = 302°
Alternatively, reflex ∠QYP = 180° + ∠XYQ
∠QYP = 180° + 122°
⇒ ∠QYP = 302°