Question

# In the adjoining figure: (i) Is ∠1 adjacent to ∠2? (ii) Is ∠AOC adjacent to ∠AOE? (iii) Do ∠COE and ∠EOD form a linear pair? (iv) Are ∠BOD and ∠DOA supplementary? (v) Is ∠1 vertically opposite to ∠4? (vi) What is the vertically opposite angle of ∠5?

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Solution

## (i) Yes. Since they have a common vertex O and also a common arm OC. Also, their non-common arms, OA and OE, are on either side of the common arm. (ii) No. They have a common vertex O and also a common arm OA. However, their non-common arms, OC and OE, are on the same side of the common arm. Therefore, these are not adjacent to each other. (iii) Yes. Since they have a common vertex O and a common arm OE. Also, their non-common arms, OC and OD, are opposite rays. (iv) Yes. Since ∠BOD and ∠DOA have a common vertex O and their non-common arms are opposite to each other. (v) Yes. Since these are formed due to the intersection of two straight lines (AB and CD). (vi) ∠COB is the vertically opposite angle of ∠5 as these are formed due to the intersection of two straight lines, AB and CD.

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