Question

In the figure AB and CD are two straight lines intersecting at O. Magnitude of ∟ is …………………

Answer 1

Answer:

Step-by-step explanation:

AB and CD intersect at O and CD is a straight line.

(i) ∠COA+ ∠AOD = 180°   (linear pair)

42°+ ∠AOD  = 180°

∠AOD  = 138°_____answer

(ii) ∠COA and ∠BOD are vertically opposite angles.  

∴∠COA = ∠BOD = 42°   [from (i)]

(iii) ∠COB and ∠AOD are vertically opposite angles.

∴∠COB = ∠AOD = 138°  [from (i)]

I think my answer is capable to clear your confusion..

hope you help it

Answer 2

Since CD is a straight line

∠COD = 180°

∠COP + ∠POB + ∠BOD = 180°

⇒ (3x + 7)° + (x + 5)° + 40° = 180°

⇒ (3x + x)° + (7 + 5 + 40)° = 180°

⇒ (4x)° + 52° = 180°

⇒ (4x)° = 180° - 52°

⇒ (4x)° = 128°

⇒ x = (128/4)° = 32°

Since AB and CD are straight lines intersecting at O,

∠AOD and ∠COB are vertically opposite angles

⇒ ∠AOD = ∠COB

=  (3x + 7)° + (x + 5)°

= (4x)° + 12°

= (4×32°) + 12°

= 128° + 12°

= 140°