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

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

$A$ triangle $ABC$ is right-angled at $A$. $L$ is a point on $BC$ such that $AL \perp BC$. Prove that $\angle BAL = \angle ACB$.

In the figure,$\angle Q > \angle R$,$PA$ is the bisector of $\angle QPR$ and $PM \perp QR$. Prove that $\angle APM = \frac{1}{2}(\angle Q - \angle R)$.