Prove that the vertically opposite angles are equal.

In the given figure, two straight line $AB$ and $CD$ intersect at a point $O$. If $\angle AOC = 42°$, find the measure of the angles $\angle AOD, \angle BOD \& \angle COB$.

In the given figure, $l\parallel m$ and $t$ is a transversal. If $\angle 1$ and $\angle 2$ are in the ratio $5:7$, find the measure of each of the angles
$\angle 1$, $\angle 2$, $\angle 3$ and $\angle 4$.

In the given figure, $\mathbf{\angle }1\mathbf{}$ and $\mathbf{}\mathbf{\angle }2\mathbf{}$ are supplementary angles. If $\mathit{\angle }1$ is decreased, what changes should take place in $\mathit{\angle }2$ so that both the angles still remain supplementary.

In the given figure, two straight line $PQ$ and $RS$ intersect at a $O$. If $\angle POS=114°$, find the measure of each of the angles $\angle POR, \angle ROQ \& \angle QOS$.

In Figure, $l\left|\right|m$ and $p\left|\right|q$. Find the values of $x, y, z, t$.

In the given figure, $AOB$ is a straight line and the rays $OC$ and $OD$ stands on it. If $\angle AOC=65°, \angle BOD=70°$ and $\angle COD = x°$, find the value of $x$.

In the given figure, $AB\parallel CD$ and $CA$ has been produced to $E$ so that $\angle BAE=125°$.
If$\angle BAC=x°$, $\angle ABD=x°$, $\angle BDC=y°$ and $\angle ACD=z°$, find the values of $x$, $y$, $z$.

In the following figure, is $\mathit{\angle }1\mathit{}$ adjacent to $\mathit{\angle }2$? Give reasons.

In the given figure, $AOB$ is a straight line and the ray $OC$ stands on it. If $\angle AOC=64°$ and $\angle BOC=x°$, find the value of $x$.