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,$PQ$ 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,if $\angle PQR = \angle PRQ$,then prove that $\angle PQS = \angle PRT$.

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,$OP$,$OQ$,$OR$,and $OS$ are four rays. Prove that $\angle POQ + \angle QOR + \angle SOR + \angle POS = 360^o$.

In the figure,$POQ$ is a line. Ray $OR$ is perpendicular to line $PQ$. $OS$ is another ray lying between rays $OP$ and $OR$. Prove that $\angle ROS = \frac{1}{2}(\angle QOS - \angle POS)$.