Angles Formed When a Transversal Cuts Two Parallel Lines

In each of the given figures, two lines $l$ and $m$ are cut by a transversal $t$.
Find whether $l\parallel m$.

In the given figure, $AB\parallel CD$ and $CA$ has been produced to $E$ so that $\angle BAE=125°$.
If$\angle BAC=x°$, $\angle ABD=x°$, $\angle BDC=y°$ and $\angle ACD=z°$, find the values of $x$, $y$, $z$.

In the given figure, $AB\parallel DC$ and $AD\parallel BC$, and $AC$ is a diagonal. If $\angle BAC=35°$,$\angle CAD=40°$, $\angle ACB=x°$, and $\angle ACD=y°$, find the value of $x$ and $y$.

In the given figure, $l\parallel m$ and $p\parallel q$.
Find the measure of each of the angles $\angle a$, $\angle b$, $\angle c$ and $\angle d$.

In the given figure, $ABCD$ is a quadrilateral in which $AB\parallel DC$ and $AD\parallel BC$.

Prove that $\angle ADC=\angle ABC$.

In the given figure, $AB\parallel CD$, $\angle ABE=120°$, $\angle ECD=100°$, and $\angle BEC=x°$.
Find the value of $x$.

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 $GL\parallel HM$.

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 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 $CE\parallel BA$, $\angle BAC=80°$ and $\angle ECD=35°$.
Find $\angle ACE$, $\angle ACB$ and $\angle ABC$.

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 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 $y$.

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, $l\parallel m$ 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 $\angle 4$.

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 $\angle 8$.