In the given figure $AS\parallel BT$, $\angle 4=\angle 5$ and $SB$ is an angle bisector of $\angle AST$, Find the value of $\angle 1$.

  

In the given figure, the side $QP$ and $RQ$ of the $∆PQR$ are extended to points $S$ and $T$ respectively. If $\angle SPR=135°$ and $\angle PQT=110°$, find the measure of $\angle PRQ$.

In the given figure $\angle ZXY=62°$ and $\angle XYZ=54°$. If $YO$ and $ZO$ are the bisectors of $\angle XYZ$ and $\angle XZY$ respectively in $∆XYZ$, find value of $\angle OZY$ and $\angle YOZ$.

In the given figure $AB\parallel DE, \angle BAC=35°$ and $\angle CDE=53°$ find the measure of $\angle DCE$.

In the given figure lines $PQ$ and $RS$ intersect at a point $T$. If $\angle PRT=40°, \angle RPT=95°$ and $\angle TSQ=75°$, find the value of $\angle SQT$.

In the figure, $AB\perp AC$, and $AB\parallel CD$, if $\angle CBD=28°, \angle BDE=65°$, find the values of $x$ and $y$.

In the adjoining figure the side $BC$ of $∆ABC$ is extended up to $D$. If the bisectors of $\angle ABC$ and $\angle ACD$ meet at a point $E$ then prove that $\angle BEC=\frac{1}{2}\angle BAC$.