Question

It is given that $\angle XYZ={64}^o$ and $XY$ is produced to point $P$. Draw a figure from the given information. If ray $YQ$ bisects $\angle ZYP$, find reflex $\angle QYP$ in degrees.

Answer 1

It is given that say $YQ$ bisects $\angle ZYP$

So let, $\angle PYQ=\angle QYZ=x$

$\angle PYZ=2x$

Since $QY$ stands on say $PX$

$\angle PYZ+\angle ZYX={180}^o$

$\Rightarrow 2x+{64}^o={180}^o$

$[\because \angle ZYX=\angle XYZ={64}^o]$

$\Rightarrow x=(180-64)/2$

$x={58}^0$

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

and reflex

$\angle QYP={360}^o-\angle QYP={360}^o-x$

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