In the given figure, $l\parallel m$ and $t$ is a transversal. If $\angle 5=70°$, find the measure of each of the angles
$\angle 1$, $\angle 3$, $\angle 4$ and $\angle 8$.

In the given figure, $l\parallel m$ and $t$ is a transversal. If $\angle 1$ and $\angle 2$ are in the ratio $5:7$, find the measure of each of the angles
$\angle 1$, $\angle 2$, $\angle 3$ and $\angle 4$.

Two parallel lines $l$ and $m$ cut by a transversal $t$. If the interior angles of the same side of t be $(2x-8)°$ and $(3x-7)°$, find the measure of each of these angles.

In the given figure, $l\parallel m$. If $s$ and $t$ be transversals such that $s$ is not parallel to $t$. Find the values of $x$ and $y$.

In the given figure, $\angle B=65°$ and $\angle C=45°$ in $∆ABC$ and $DAE\parallel BC$. If $\angle DAB=x°$ and $\angle EAC=y°$, find the values of $x$ and  $y$.

In the adjoining figure, it is given that $CE\parallel BA$, $\angle BAC=80°$ and $\angle ECD=35°$.
Find $\angle ACE$, $\angle ACB$ and $\angle ABC$.

In the adjoining figure, it is given that $AO\parallel CD$, $OB\parallel CE$, and $\angle AOB=50°$. Find the measure of $\angle ECD$

In the adjoining figure, it is given that $AB\parallel CD$, $\angle ABO=50°$, $\angle CDO=40°$. Find the measure of $\angle BOD$.

In the given figure, $AB\parallel CD$ and a transversal $EF$ cuts them at $G$ and $H$ respectively.
If $GL$ and $HM$ are the bisectors of the alternate angles $\angle AGH$and $\angle GHD$ respectively, prove that $GL\parallel HM$.