Question

Diagonals AC and BD of a parallelogram ABCD intersect each other at point 0 If DAC 30 and AOB = 80 , then find the measure of LDBA. - pls answer it is very important for me
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Answer 1

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

∘

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 ∘

Please mark me as brainliest. I have only 5 brainliest answers to become Ace.