Properties of Parallel Lines

In the figure, line $l\parallel$ line $m$ and line $n\parallel$ line $p$. Find $\angle a, \angle b, \angle c$  from the given measure of an angle.

In the figure, line $p\parallel$ line $q$ and line $l$ and line $m$ are transversals. Measures of some angles are shown. Hence find the measures of $\angle a, \angle b, \angle c, \angle d.$

In the figure, if ray $BA\parallel$ray $DE$, $\angle C=50°$ and $\angle D=100°$. Find the measure of $\angle ABC$ in degrees $\left(°\right)$.

In the figure, line $AB\parallel$ line $CD$ and line $PQ$ is transversal. Measure of one of the angles is given. Hence find the measures of $\angle PRB$ in degrees $\left(°\right)$.

In the figure, line $AB\parallel$ line $CD$ and line $PQ$ is transversal. Measure of one of the angles is given. Hence find the measures of $\angle DTQ$ in degrees $\left(°\right)$. (Write the numerical value)

In the figure, line $AB\parallel$ line $CD$ and line $PQ$ is transversal. Measure of one of the angles is given. Hence find the measures of $\angle CTQ$ in degrees $\left(°\right)$.

In the figure, line $AB\parallel$ line $CD$ and line $PQ$ is transversal. Measure of one of the angles is given. Find the measures of $\angle ART$. (Write the answer without degrees $\left(°\right)$  symbol)

In the figure, line $RP\parallel$ line $MS$ and line $DK$ is their transversal. $\angle DHP=85°$.

The measure of angle $\angle MGK$ is _____ $°.$

In the figure, line $RP\parallel$ line $MS$ and line $DK$ is their transversal. $\angle DHP=85°$. If the measure of angle $\angle HGS=x°$, then write the value of $x$.

In the figure, line $RP\parallel$ line $MS$ and line $DK$ is their transversal. $\angle DHP=85°$.

Find the measure of angle $\angle PHG$ in degree $\left(°\right).$

In the figure, line $RP\parallel$ line $MS$ and line $DK$ is their transversal. $\angle DHP=85°$. If the measure of $\angle RHD$ is $z°$, then find $z$.

In the figure, ray $AE\parallel$ ray $BD$, ray $AF$ is the bisector of $\angle EAB$ and ray $BC$ is the bisector of $\angle ABD$. Prove that line $AF\parallel$ line $BC$.

A transversal $EF$ of line $AB$ and line $CD$ intersects the lines at point $P$ and $Q$, respectively. Ray $PR$ and ray $QS$ are parallel and bisectors of $\angle BPQ$ and $\angle PQC$. respectively. Prove that line $AB\parallel$ line $CD$

In the figure, if $\angle a\cong \angle b$ and $\angle x\cong \angle y$, then prove that line $l\parallel$ line $n$.

In figure, if $\angle a\cong \angle b$, then prove that line $l\parallel$ line $m$.

In figure, sides of $\angle PQR$ and $\angle XYZ$ are parallel to each other. Prove that, $\angle PQR\cong \angle XYZ$.

In the figure, $y=108°$ and $x=71°$ . Are the lines $m$ and $n$ parallel? Justify?