1.

The diagonals AC and BD of aparallelogram ABCD intersect each other atthe point o. If CAD = 32° and AOB = 70°,find DBC.​

Answer»

ANSWER:

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

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⇒∠OBC + 110

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+ 32

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= 180

∘

⇒ ∠OBC = 38

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∴ ∠DBC = 38

∘


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