Mathematics

In the figure (IMAGE)

(a)   Is $$ \angle 1$$ 

adjacent to $$ \angle 2 $$?

(b)  Is $$ \angle AOC $$ 
adjacent to $$ \angle AOE $$?

(c)   Do $$ \angle COE $$ and $$ \angle EOD $$ from  linear pair?

(d)  Are $$ \angle BOD $$ and $$ \angle DOA $$
supplementary?

(e)  is $$ \angle 1 $$ vertically opposite to $$ \angle 4$$?

(f)   What  is the vertically opposite angle of $$ \angle 5$$?


SOLUTION
In the figure given,
(a) Yes. $$\angle 1$$ is adjacent to $$\angle 2$$ because arm $$AO$$ is adjacent to arm $$OC$$.

(b) No.  >$$\angle AOC$$ is not adjacent to $$\angle AOE$$ because $$\angle AOC$$ is inside $$\angle AOE$$.

(c) Yes. $$\angle COE$$ and $$\angle EOD$$ form a linear pair because we can see that $$CD$$ is a straight line.

(d) Yes. $$\angle BOD$$ and $$\angle DOA$$ are supplementary angles because angle between them is $$180^{\circ}$$.

(e) Yes. $$\angle 1$$ is vertically opposite to $$\angle 4$$ because $$AB$$ and $$CD$$ are straight lines.

(f) $$\angle 2+\angle 3$$ are vertically opposite to $$\angle 5$$ because $$AB$$ and $$DC$$ are straight lines which intersect at $$O$$.
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