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The diagonals AC and BD of a parallelogr...

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O such that `angle DAC =30^(@) and angle AOB=70^(@), " Then, " angle DBC=`?

A

`40^(@)`

B

`35^(@)`

C

`45^(@)`

D

`50^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
`angle AOC = angle DAC =30^(@) " "("alt. interior "angle )`
`rArr angle OCB =30^(@)`.
`angle AOB+angle BOC=180^(@) rArr 70^(@) + angle BOC =180^(@) rArr angle BOC=110^(@).`
In `triangle OBC, angle BOC +angle OCB + angle OBC =180^(@)`
`rArr 110^(@)+30^(@)+angle OBC =180^(@) rArr angle OBC =40^(@).`
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