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In the adjoining figure:
$(i)$ Is $\angle 1$ adjacent to $\angle 2$?
$(ii)$ Is $\angle AOC$ adjacent to $\angle AOE$?
$(iii)$ Do $\angle COE$ and $\angle EOD$ form a linear pair?
$(iv)$ Are $\angle BOD$ and $\angle DOA$ supplementary?
$(v)$ Is $\angle 1$ vertically opposite to $\angle 4$?
$(vi)$ What is the vertically opposite angle of $\angle 5$?
To do:
We have to answer the given questions by observing the given figure.
Solution:
(i) Yes, $\angle 1$ and $\angle 2$ are adjacent angles.
$\angle 1$ and $\angle 2$ have a common vertex $O$, a common arm $OC$ and $OA$ and $OE$ are on both sides of the common arm $OC$.
(ii) No, $\angle AOC$ is not adjacent to $\angle AOE$
$OC$ and $OE$ do not lie on either side of the common arm $OA$.
(iii) Yes, $\angle COE$ and $\angle EOD$ form a linear pair.
$CO$ and $OD$ form a straight line and the sum of $\angle COE$ and $\angle EOD$ is $180^o$
(iv) Yes, $\angle BOD$ and $\angle DOA$ are supplementary.
$\angle BOD$ and $\angle DOA$ have a common vertex $O$, a common arm $OD$ and $OA$ and $OB$ are on both sides of the common arm $OD$.
(v) Yes, $\angle 1$ is vertically opposite to $\angle 4$.
(vi) Vertically opposite angle of $\angle 5$ is $\angle BOC$.