In the figure,$AB \parallel CD$ and $CD \parallel EF$. Also,$EA \perp AB$. If $\angle BEF = 55^o$,find the values of $x, y$,and $z$.

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

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 $^\circ$)

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 $AB \parallel CD$,$EF \perp CD$ and $\angle GED = 126^o$,find $\angle AGE$,$\angle GEF$ and $\angle FGE$.