In the figure,lines $XY$ and $MN$ intersect at $O$. If $\angle POY = 90^o$ and $a: b = 2: 3$,find $c$. (in $^o$)

In the figure,if $PQ \parallel RS$,$\angle MXQ = 135^o$ and $\angle MYR = 40^o$,find $\angle XMY$. (in $^o$)

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,$\angle X = 62^o$ 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,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 $^\circ$)

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 $^o$)