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In the given figure, AB||CD, angleABE=12...

In the given figure, `AB||CD, angleABE=120^(@), angleECD=100^(@)` and `angleBEC=x^(@)`. Find the value of x.

A

`x=30`

B

`x=20`

C

`x=50`

D

`x=40`

Text Solution

Verified by Experts

The correct Answer is:
D
Through E, draw `FEG||AB||CD`. Now, `FE||AB` and BE is the transversal.
`:. angleBEF+angleABE=180^(@)` [co-interior `angles`]
`implies angleBEF+120^(@)=180^(@)`
`implies angleBEF=(180^(@)-120^(@))=60^(@)`.
Again `CD||EG` and CE is the transversal.
`:. angleCEG+angleECD=180^(@)` [co-interior `angles`]
`implies angleCEG+100^(@)=180^(@)`
`implies angleCEG=(180^(@)-100^(@))=80^(@)`.
Now, FEG is a straight line.
`:. angleBEF+angleBEC+angleCEG=180^(@)`
`implies 60^(@)+x^(@)+80^(@)=180^(@) implies x+140=180 implies x=40`.
Hence, `x=40`.
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