If two angles have a common vertex and their arms form opposite rays (

1.	If two angles have a common vertex and their arms form opposite rays (figure). Then,(a) how many angles are formed?(b) how many types of angles are formed?(c) write all the pairs of vertically opposite angles.
Answer» (a) Total 13 angles are formed, namely ∠AOB, ∠BOC, ∠COD, ∠DOA, ∠AOC, ∠BOD, ∠DOB, ∠AOD, ∠BOA, ∠COB, ∠DOC, ∠AOA. (b) Following types of angles are formed: (i) Linear pair (ii) Supplementary (iii) Vertically opposite (iv) Adjacent (c) Following are the pair of vertically opposite angles: ∠1, ∠3; ∠2, ∠4.

If two angles have a common vertex and their arms form opposite rays (figure). Then,(a) how many angles are formed?(b) how many types of angles are formed?(c) write all the pairs of vertically opposite angles.

Answer»

(a) Total 13 angles are formed, namely ∠AOB, ∠BOC, ∠COD, ∠DOA, ∠AOC, ∠BOD, ∠DOB, ∠AOD, ∠BOA, ∠COB, ∠DOC, ∠AOA.

(b) Following types of angles are formed:

(i) Linear pair
(ii) Supplementary
(iii) Vertically opposite
(iv) Adjacent

(c) Following are the pair of vertically opposite angles:

∠1, ∠3; ∠2, ∠4.