In the figure, AB is parallel to CD, find $x$.

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

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 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.

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, 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, 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, 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 $c.$

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

 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 $90°$.

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

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 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 $m$.

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