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Q.9 In the following 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 angle to angle 4?
(vi) What is the vertically opposite angle of \(\angle \) 5?

Answer :

(i) Yes, \(\angle \) 1 and \(\angle \) 2 are adjacent angles.
because it's one arm (OC) is common
(ii) No, \(\angle \) AOC is not adjacent to \(\angle \) AOE.
[ because OC and OE do not lie on either side of common arm OA] .
(iii) Yes, \(\angle \) COE and \(\angle \) EOD form a linear pair of angles.
(iv) Yes, \(\angle \) BOD and \(\angle \) DOA are supplementary.
[Because \(\angle \) BOD + because \(\angle \)DOA = 180°]
(v) Yes, \(\angle \) 1 is vertically opposite to \(\angle \) 4.
(vi) Vertically opposite angle of \(\angle \) 5 is \(\angle \) 2 + \(\angle \) 3 i.e. angle BOC.