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

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

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Given that,
\angleXYZ = 64^0 and XY produced to point P and Ray YQ bisects \angleZYP  \Rightarrow \angle QYP = \angle ZYQ
Now, XYP is a straight line
So, \angleXYZ + \angleZYQ + \angleQYP = 180^0
\Rightarrow 2(\angle QYP )=180^0 - 64^0 = 116^0
\Rightarrow (\angle QYP )= 58^0

Thus reflex of \angleQYP = 360^0- 58^0 = 302^0

Since \angleXYQ = \angleXYZ + \angleZYQ  [\because \angle QYP = \angle ZYQ


    \angle XYQ64^0+58^0 = 122^0

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