EXERCISE 6.2

In the adjoining figure, find the value of $x$.

In the adjoining figure, $\angle AOC=\left(2y-13\right)°$ and $\angle BOC=\left(3y-12\right)°$, find all the four angles.

Prove that the bisectors of a vertically opposite angles are in the same straight line.

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

From a point $O$ in a line $AB,$ ray $OC$ and $OD$ are drawn on opposite sides of $AB$ such that $\angle BOC=\angle AOD$. Prove that $OC$ and $OD$ are opposite rays.