In the figure,if $AB \parallel CD$,$CD \parallel EF$ and $y: z = 3: 7$,find $x$. (in $^o$)

In the figure,the sides $AB$ and $AC$ of $\Delta ABC$ are produced to points $E$ and $D$ respectively. If the bisectors $BO$ and $CO$ of $\angle CBE$ and $\angle BCD$ respectively meet at point $O$,then prove that $\angle BOC = 90^o - \frac{1}{2} \angle BAC$.

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

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 $^o$)

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

If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel,then prove that the two lines are parallel.