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,sides $QP$ and $RQ$ of $\Delta PQR$ are produced to points $S$ and $T$ respectively. If $\angle SPR = 135^o$ and $\angle PQT = 110^o$,find $\angle PRQ$. (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 $PQ \parallel ST$,$\angle PQR = 110^o$ and $\angle RST = 130^o$,find $\angle QRS$. (in $^o$)

In the figure,lines $AB$ and $CD$ intersect at $O$. If $\angle AOC + \angle BOE = 70^o$ and $\angle BOD = 40^o$,find $\angle BOE$ and reflex $\angle COE$.

In the figure,if $QT \perp PR$,$\angle TQR = 40^o$ and $\angle SPR = 30^o$,find $x$ and $y$.