Question

Q. The diagonals AC and BD of a parallelogram ABCD intersect each other
at the point o such that LDAC = 30° and LAOB =70°, then LDBC = ?
309
70
A
B​

Answer 1

Answer:

In given figure,

Quadrilateral ABCD is a parallelogram.

So, AD ∣∣ BC

∴ ∠DAC = ∠ACB  --- ( Alternate angle)

∴ ∠ACB = 32  

∠AOB + ∠BOC = 180  --- (straight angle)

⇒70  + ∠BOC = 180  

∴ ∠BOC = 110  

 

In △BOC,

∠OBC + ∠BOC + ∠OCB = 180  

⇒∠OBC  + 110  + 32  ∘

= 180  

⇒ ∠OBC = 38  

∴  ∠DBC = 38  

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Answer 2

In given figure,

Quadrilateral ABCD is a parallelogram.

So, AD ∣∣ BC

∴ ∠DAC = ∠ACB --- ( Alternate angle)

∴ ∠ACB = 32

∘

∠AOB + ∠BOC = 180

∘

--- (straight angle)

⇒70

∘

+ ∠BOC = 180

∘

∴ ∠BOC = 110

∘

In △BOC,

∠OBC + ∠BOC + ∠OCB = 180

∘

⇒∠OBC + 110

∘

+ 32

∘

= 180

∘

⇒ ∠OBC = 38

∘

∴ ∠DBC = 38

∘