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In the adjoining figure, ABCD is a rhomb...

In the adjoining figure, ABCD is a rhombus. If `angle A =70^(@), " find " angle CDB. `

A

`angle CDB = 85^(@).`

B

`angle CDB = 75^(@).`

C

`angle CDB = 55^(@).`

D

`angle CDB = 65^(@).`

Text Solution

Verified by Experts

The correct Answer is:
C
We have `angle C = angle A = 70^(@) " " ("opposite " angle " of a || gm").`
Let `angle CDB =x^(@)`.
In `triangle CDB, ` we have
`CD=CB rArr angle CBD = angle CDB=x^(@).`
` therefore angle CDB + angle CBD +angle DCB=180^(@) " " ("sum of " angle " of a " triangle )`
`rArr x^(@) +x^(@) +70^(@) =180^(@) rArr 2x=110,i.e., x=55.`
Hence, `angle CDB = 55^(@).`
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