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.

It is given in the question that:

∠XYZ = 64^o

YQ bisects ∠ZYP

∠XYZ + ∠ZYP = 180^o (Linear pair)

64^o + ∠ZYP = 180^o

∠ZYP = 116^o

And,

∠ZYP = ∠ZYQ + ∠QYP

∠ZYQ = ∠QYP (YQ bisects ∠ZYP)

∠ZYP = 2∠ZYQ

2∠ZYQ = 116^o

∠ZYQ = 58^o = ∠QYP

Now,

∠XYQ = ∠XYZ + ∠ZYQ

∠XYQ = 64^o + 58^o

∠XYQ = 122^o

And,

Reflex of ∠QYP = 180^o + ∠XYQ

∠QYP = 180^o + 122^o

∠QYP = 302^o