# 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.

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

Thus reflex of $\angle$QYP = $360^0- 58^0 = 302^0$

Since $\angle$XYQ = $\angle$XYZ + $\angle$ZYQ  [$\because$ $\angle QYP = \angle ZYQ$

$\angle XYQ$$64^0+58^0 = 122^0$

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