In the given figure, $AB\parallel CD$. Find the value of $x$.

In the given figure, $AB\parallel CD$. Find the value of $x, y$ and $z$.

In the given figure, $AB\parallel CD$. Prove that $\angle BAE-\angle ECD=\angle AEC$

In the given figure, $AB\parallel CD$. Prove that$p+q-\mathrm{r}=180$

In the given figure, $AB\parallel CD$ and $EF\parallel GH$ Find the values of $x\mathit{,}\mathit{ }y\mathit{,}\mathit{ }z$ and $t$.

In the given figure, $AB \left|\right| CD$ and a transversal $t$ cuts them at $E$ and $F$ respectively. If $EG$ and $FG$ are the bisectors of $\angle BEF$ and $\angle EFD$ respectively, prove that $\angle \mathrm{EGF}=90°$.

 In the given figure,$AB \left|\right| CD$ and a transversal $t$ cuts them at $E$ and $F$ respectively. If $EP$ and $FQ$ are the bisectors of $\angle AEF$ and $\angle EFD$ respectively, prove that $EP \left|\right| FQ$.

In the given figure, $BA \left|\right| ED$ and $BC \left|\right| EF$. Show that $\angle ABC = \angle DEF.$

In the given figure, $BA \left|\right| ED$ and $BC \left|\right| EF$. Show that $\angle ABC+\angle DEF=180°$