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In the given figure, AB||CD, angleABO=40...

In the given figure, `AB||CD, angleABO=40^(@), angleCDO=35^(@)`. Find the value of the reflex `angleBOD` and hence the value of x.

A

283

B

284

C

285

D

286

Text Solution

Verified by Experts

The correct Answer is:
C
Through O, draw `EO||AB||Cd`.
Then, `angleEOB+angleEOD=x^(@)`.
Now, `AB||EO` and BO is the transversal.
`:. angleABO+angleBOE=180^(@)` [consecutive int. `angles`]
`implies 40^(@)+angleBOE=180^(@)`
`implies angleBOE=(180^(@)-40^(@))=140^(@)`.
Again, `CD||EO` and OD is the transversal.
`:. angleEOD+angleODC=180^(@)`
`implies angleEOD+35^(@)=180^(@)`
`implies angleEOD=(180^(@)-35^(@))=145^(@)`.
`:.` reflex `angleBOD=x^(@)=(angleBOE+angleEOD)`
`=(140^(@)+145^(@))=285^(@)`.
Hence, `x=285`.
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