In the given figure, the two lines $AB$ and $CD$ intersect at a point $O$ such that $\angle BOC=125°.$ Find the values of $x, y \mathrm{and} z$.

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.

Prove that the bisectors of two adjacent supplementary angles include a right angle.

In the given figure, $l \Vert m$ and a transversal $t$ cuts them. If $\angle 1=120°,$ find the measure of each of the remaining marked angles.

In the given figure, $l \Vert m$ and a transversal $t$ cuts them. If $\angle 7=80°,$ find the measure of each of the remaining marked angles.

In the given figure, $l \Vert m$ and a transversal $t$ cuts them. If $\angle 1:\angle 2=2:3,$ find the measure of each of the marked angles.

For what value of $x\mathit{ }$will the lines$\mathit{ }l\mathit{ }$and $m$ be parallel to each other?

For what value of $\mathrm{x}$ will the lines $l$ and $m$ be parallel to each other?

In the given figure, $AB\parallel CD$ and $BC\parallel ED$. Find the value of $x$.