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

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It is given that line YQ bisects PYZ.

Hence, QYP = ZYQ

It can be observed that PX is a line. Rays YQ and YZ stand on it.

XYZ + ZYQ + QYP = 180º

64º + 2QYP = 180º

2QYP = 180º − 64º = 116º

QYP = 58º

Also, ZYQ = QYP = 58º

Reflex QYP = 360º − 58º = 302º

XYQ = XYZ + ZYQ

= 64º + 58º = 122º

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