In the given figure three lines $\overrightarrow{\mathrm{AB}},\overrightarrow{ \mathrm{CD}}$ and $\overrightarrow{\mathrm{EF}}$ intersecting at $O$. Find the values of $x, y$ and $z$. it is being given that $x:y:z=2:3:5$.

As shown in figure if $\mathrm{\angle }POR:\mathrm{\angle }ROQ=5:7$ then $\angle SOQ=\_\_\_$.

Consider the following statements when two straight lines intersect :
i) Adjacent angles are complementary.
ii) Adjacent angles are supplementary.
iii) Vertically opposite angles are equal.
iv) Vertically opposite angles are supplementary.

If $ABC$ is a straight line then value of $x$, in the given diagram will be 

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

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