Question

It is given that $\angle XYZ={64}^{\circ }$ 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$\angle QYP$

Answer 1

$XYP$ is a straight line,

$\angle XYZ+\angle ZYP={180}^{\circ }$(linear pair)

$\angle ZYP={180}^{\circ }-\angle XYZ={180}^{\circ }-{64}^{\circ }={116}^{\circ }$

Since $YQ$ bisects $\angle ZYP$

$\angle ZYQ=\angle QYP=\frac{1}{2}\angle ZYP=\frac{1}{2}\times {116}^{\circ }={58}^{\circ }$

$\angle XYQ=\angle XYZ+\angle ZYQ={64}^{\circ }+{58}^{\circ }={122}^{\circ }$

We have to find reflex$\angle QYP$

Reflex$\angle QYP={360}^{\circ }-\angle QYP={360}^{\circ }-{58}^{\circ }={302}^{\circ }$