It is given that $\angle XYZ = 64^o$ and $XY$ is produced to point $P$. If ray $YQ$ bisects $\angle ZYP$,find $\angle XYQ$ and reflex $\angle QYP$. (in $^o$)

In the figure,if $AB \parallel CD$,$EF \perp CD$ and $\angle GED = 126^o$,find $\angle AGE$,$\angle GEF$ and $\angle FGE$.

In the figure,if $\angle PQR = \angle PRQ$,then prove that $\angle PQS = \angle PRT$.

In the figure,if $AB \parallel DE$,$\angle BAC = 35^o$ and $\angle CDE = 53^o$,find $\angle DCE$. (in $^o$)

In the figure,if $QT \perp PR$,$\angle TQR = 40^o$ and $\angle SPR = 30^o$,find $x$ and $y$.

In the figure,the sides $AB$ and $AC$ of $\Delta ABC$ are produced to points $E$ and $D$ respectively. If the bisectors $BO$ and $CO$ of $\angle CBE$ and $\angle BCD$ respectively meet at point $O$,then prove that $\angle BOC = 90^o - \frac{1}{2} \angle BAC$.