In the figure,if $AB \parallel CD$,$\angle BMX = 125^{\circ}$ and $\angle CNX = 55^{\circ}$,find $\angle MXN$. (in $^{\circ}$)

In the following figure,ray $YW$ stands on a line $XYZ$. $\angle WYZ : \angle WYX = 1 : 2$. Ray $YQ$ and ray $YP$ are angle bisectors of $\angle WYZ$ and $\angle WYX$ respectively. Find $\angle PYQ$. (in $^{\circ}$)

In the given figure,if $PQ \parallel RS$ and $RS \parallel TU$,and $y: z = 7: 8$,find $x$.

In the figure,$AB$,$CD$,and $EF$ are three lines concurrent at $O$. Find the value of $y$. (in $^{\circ}$)

Prove that through a given point,we can draw only one perpendicular to a given line.

In the given figure,if $PQ \parallel RS$,$YZ \perp RS$ and $\angle SZX = 143^{\circ}$,then find $\angle PXZ$,$\angle XZY$ and $\angle YXZ$.