What is linear pair?

In figure, if $\mathrm{AB}\parallel \mathrm{CD}, \mathrm{CD}\parallel \mathrm{EF}$ and $y:z=4:5,$ then find the value of $x.$

In the adjoining figure, three coplanar lines $\mathrm{AB}, \mathrm{CD} \mathrm{and} \mathrm{EF}$ intersect at a point $\mathrm{O},$ forming angles as shown. Find the values of $\mathrm{x}, \mathrm{y}, \mathrm{z} \mathrm{and} \mathrm{t}.$

In the given figure, if $x+y=w+z$, then prove that $AOB$ is a line.

If two straight lines intersect each other then prove that the ray opposite to the bisector of one of the angles so formed bisects the vertically opposite angle.

In figure, measures of some angles are shown. Using the measures find the measures of $\angle x$ and $\angle y$. Hence show that line $l \parallel$ line $m$.

In the given figure, if $AB\parallel CD, EF\perp CD$ and $\mathrm{\angle }GED=126°,$ find $\mathrm{\angle }AGE, \mathrm{\angle }GEF$ and $\mathrm{\angle }FGE.$

Two adjacent angles on a straight line are in the ratio$5:4$. Find the measure of each of these angles.

Two lines$\mathrm{AB} \mathrm{and} \mathrm{CD}$ intersect at a point $\mathrm{O}$such that $\angle \mathrm{BOC}+\angle \mathrm{AOD}=280°$, as shown in the figure. Find all the four angles.

In the given figure, find the value of $\mathrm{\angle }\mathrm{EOD}$.

In the adjoining, three coplanar lines $AB\mathit{,}\mathit{ }CD$ and $\mathit{ }EF$ intersect at a point $O$. Find the value of$\mathrm{x}$. Hence, $\mathit{\angle }AOD\mathit{,}\mathit{ }\mathit{\angle }COE$ and $\mathit{\angle }AOE$

In the given figure, ray $OC$ is the bisector of $\angle AOB$ and $OD$ is the ray opposite to $OC$. Show that $\angle AOD=\angle BOD$.

Two lines $AB$ and $CD$ intersect at $\mathrm{O}$. If $\angle \mathrm{AO}C=50°$, find $\angle \mathrm{AOD}, \angle \mathrm{BOD}$ and $\angle \mathrm{BOC}$.

 If two straight lines intersect each other in such a way that one of the angles formed measure$90°$, show that each of the remaining angles measures $90°$.

In the given figure, lines $\mathrm{X}\mathrm{Y}$ and $\mathrm{M}\mathrm{N}$ intersect at $\mathrm{O}.$ If $\mathrm{\angle }\mathrm{P}\mathrm{O}\mathrm{Y}=90°$ and $a:b=2:3,$ find $c.$