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 $\angle XYQ$ and reflex $\angle QYP$

Answer 1

As angle on a line $={180}^o$

$\Rightarrow \angle XYZ+\angle PYZ={180}^o$

$\Rightarrow \angle PYZ=180-64={116}^o$

As YQ bisects $\angle PYZ$

$\Rightarrow ZYA=\angle QYP={58}^o$

$\Rightarrow XYQ=64+58={122}^o$,

reflex $\angle QYP-{360}^o-\angle QYP$

$=360-58={302}^o$.