Using the figure, answer the following questions and justify your answ

1.	Using the figure, answer the following questions and justify your answer. (i) Is ∠1 adjacent to ∠2? (ii) Is ∠AOB adjacent to ∠BOE? (iii) Does ∠BOC and ∠BOD form a linear pair? (iv) Are the angles ∠COD and ∠BOD supplementary. (v) Is ∠3 vertically opposite to ∠1 ?
Answer» (i) Yes, ∠1 is adjacent to ∠2. Because they both have the common vertex ‘O’ and the common arm OA . Also their interiors do not overlap. (ii) No, ∠AOB and ∠BOB are not adjacent angles because they have overlapping interiors. (iii) No, ∠BOC and ∠BOD does not form a linear pair. Because ∠BOC itself a straight angle, so the sum of ∠BOC and ∠BOD exceed 180°. (iv) Yes, the angles ∠COD and ∠BOD are supplementary ∠COD + ∠BOD = 180°, [∵ linear pair of angles] ∴ ∠COD and ∠BOD are supplementary. (v) No. ∠3 and ∠1 are not formed by intersecting lines. So they are not vertically opposite angles.

Using the figure, answer the following questions and justify your answer. (i) Is ∠1 adjacent to ∠2? (ii) Is ∠AOB adjacent to ∠BOE? (iii) Does ∠BOC and ∠BOD form a linear pair? (iv) Are the angles ∠COD and ∠BOD supplementary. (v) Is ∠3 vertically opposite to ∠1 ?

Answer»

(i) Yes, ∠1 is adjacent to ∠2.

Because they both have the common vertex ‘O’ and the common arm OA . Also their interiors do not overlap.

(ii) No, ∠AOB and ∠BOB are not adjacent angles because they have overlapping interiors.

(iii) No, ∠BOC and ∠BOD does not form a linear pair.

Because ∠BOC itself a straight angle, so the sum of ∠BOC and ∠BOD exceed 180°.

(iv) Yes, the angles ∠COD and ∠BOD are supplementary ∠COD + ∠BOD = 180°, [∵ linear pair of angles]

∴ ∠COD and ∠BOD are supplementary.

(v) No. ∠3 and ∠1 are not formed by intersecting lines. So they are not vertically opposite angles.