Parallel Lines and a Transversal

In the given diagram, $AB\parallel CD$ and $BC\parallel ED$. Then find the value of $x$.

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

Define a Transversal Line. In adjoining figure $l\parallel m$ is cut by the transversal $t$. If $\angle 2=70°$, find the measure of $\angle 8$.

Define a Transversal Line. In adjoining figure $l\parallel m$ is cut by the transversal $t$. If $\angle 1=70°$, find the measure of $\angle 7$.

Define a Transversal Line. In adjoining figure $l\parallel m$ is cut by the transversal $t$. If $\angle 1=70°$, find the measure of $\angle 3,$ and $\angle 5$.

In the given figure, $\mathrm{BAD}\parallel \mathrm{EF}, \angle \mathrm{AEF}=55°$ and $\angle \mathrm{ACB}=25°$. If $\angle \mathrm{ABC}=\mathrm{k}°$, then find the value of $\mathrm{k}$.

In the given figure, $l \parallel \mathrm{m}$ and $n$ is a transversal. If $\angle 1=\left(5x+25\right)°$ and $\angle 2=\left(15x-35\right)°$, then find the value of $x$.

In the given figure, $\mathrm{BAD}\parallel \mathrm{EF}, \angle \mathrm{AEF}=55°$ and $\angle \mathrm{ACB}=25°$. If $\angle \mathrm{ABC}=\mathrm{k}°$, then find the value of $\mathrm{k}$.

In the following figure $\mathrm{AB}\left|\right|\mathrm{CD}$. Find the value of $x$.

In the adjacent figure, it is given that, $\mathrm{BC}\parallel \mathrm{DE}, \angle \mathrm{BAC}=35° \mathrm{and} \angle \mathrm{BCE}=102°$. If the measure of $\angle \mathrm{CED}=k°$ then find $k$.

In the adjacent figure, it is given that, $\mathrm{BC}\parallel \mathrm{DE}, \angle \mathrm{BAC}=35° \mathrm{and} \angle \mathrm{BCE}=102°$. If the measure of $\angle \mathrm{ADE}=k°$ then find $k$.

In the given figure segments shown by arrow heads are parallel. Find the values of $x$ and $y$.

Find the values of $x, y$ for which the lines $\mathrm{AD}$ and $\mathrm{BC}$ become parallel.

In the adjacent figure $\mathrm{BE}\perp \mathrm{DA}$ and $\mathrm{CD}\perp \mathrm{DA}$ then prove that $m\angle 1\cong m\angle 3$.

In the given figure $\mathrm{AB}\parallel \mathrm{CD}; \mathrm{BC}\parallel \mathrm{DE}$ then find the values of $x$ and $y$.

The measures of $a$ and $b$ are: