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In the adjoining figure : Is angle 1 adjacent to angle 2 ?

9. 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 ?

 

                                                 

 

                                                            

           

                                                       

Answers (1)
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(i) Yes, \angle 1 adjacent to \angle 2 as these have the same vertex and have one common arm.

(ii)  No,  \angle AOC is not adjacent to \angle AOE. This is because \angle AOE contains \angle AOC.

(iii) Yes the given angles form a linear pair as they are pair of supplementary angles.

(iv) Since BOA is a straight line thus the given angles are supplementary.

(v) Yes, \angle 1 and \angle 4 are vertically opposite angles as they are the angles formed by two intersecting straight lines.

(vi) The vertically opposite angle to \angle 5 is    \left ( \angle 2\ +\ \angle 3 \right ).

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