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

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 $\angle AOD=\angle BOD$.

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 $x+y=w+z$, then prove that $AOB$ is a line.

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

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 $c.$

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 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 $\mathrm{x}, \mathrm{y}, \mathrm{z} \mathrm{and} \mathrm{t}.$

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.

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 $90°$.