Measurement of Unknown Angles With Help of Parallel Lines

When two coplanar lines are cut by a transversal, which condition does not guarantee that the two lines are parallel.

In the following figure if$\angle 1=110°$ and $\angle 6=70°$ , prove $l\parallel m$.

In the following figure if$\angle 3=60°$ and $\angle 5=60°$ , prove $l\parallel m$.

In the following figure if$\angle 1=110°$ and $\angle 6=70°$ , prove $l\parallel m$.

In the following figure if$\angle 3=60°$ and $\angle 6=120°$ , prove $l\parallel m$.

In the following figure if$\angle 2=110°$ and $\angle 6=110°$ , prove $l\parallel m$.

In the following figure if$\angle 1=135°$ and $\angle 8=45°$ , prove $l\parallel m$.

Use alternate exterior angle theorem to prove that line $1$ and $2$ are parallel lines.

For the figure $\angle a=\angle b=55°$, find the relation between $AB$ and $CD$

In the given figure, find the relation between $x$ and $y$.

For the figure $\angle b=\angle d=35°$, then $PQ$ is _____ to $XY$.

Find the relation of the lines $AB$ and $CD$ when $\angle a=\angle c$

Given that $\angle \mathrm{AEC}=50°$ ,$\mathrm{AB} = \mathrm{BC}, \mathrm{AOE}$ is the diameter, find $\angle \mathrm{AOB}$. Hence, show that $\mathrm{BO}\left|\right|\mathrm{CE}$.

$\mathrm{P}$ is the midpoint of an arc $\mathrm{APB}$ of a circle. Prove that the tangent drawn at $\mathrm{P}$ will be parallel to the chord $\mathrm{AB}.$

In a cyclic quadrilateral $\mathrm{ABCD},$ the diagonal $\mathrm{AC}$ bisects the angle $\mathrm{BCD}.$ Prove that the diagonal $\mathrm{BD}$ is parallel to the tangent to the circle at point $\mathrm{A}.$

In the figure, $l\parallel m$. Prove that $\angle 1$ and $\angle 2$ are equal. Give reason.

In figure $\mathrm{AB}\parallel \mathrm{CD}$ and $\mathrm{CD}\parallel \mathrm{EF}$. Is $\mathrm{AB}\parallel \mathrm{EF}$? Give reason.

The measurements of angles of rectangle $\mathrm{ABCD}$ have written in the figure:

The measurements of angles of rectangle $\mathrm{ABCD}$ have written in the figure:

Is $\mathrm{AB}\parallel \mathrm{CD}$? If yes, then why?