In the figure,$\angle X = 62^o$ and $\angle XYZ = 54^o$. If $YO$ and $ZO$ are the bisectors of $\angle XYZ$ and $\angle XZY$ respectively of $\Delta XYZ$,find $\angle OZY$ and $\angle YOZ$.

In the figure,$PQ$ and $RS$ are two mirrors placed parallel to each other. An incident ray $AB$ strikes the mirror $PQ$ at $B$,the reflected ray moves along the path $BC$ and strikes the mirror $RS$ at $C$ and again reflects back along $CD$. Prove that $AB \parallel CD$.

In the figure,ray $OS$ stands on a line $POQ$. Ray $OR$ and ray $OT$ are angle bisectors of $\angle POS$ and $\angle SOQ$,respectively. If $\angle POS = x$,find $\angle ROT$. (in $^o$)

In the figure,lines $AB$ and $CD$ intersect at $O$. If $\angle AOC + \angle BOE = 70^o$ and $\angle BOD = 40^o$,find $\angle BOE$ and reflex $\angle COE$.

In the figure,if lines $PQ$ and $RS$ intersect at point $T$,such that $\angle PRT = 40^\circ$,$\angle RPT = 95^\circ$ and $\angle TSQ = 75^\circ$,find $\angle SQT$. (in $^\circ$)

In the figure,find the values of $x$ and $y$ and then show that $AB \parallel CD$.