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In the given figure, AB||CD and angleAOC...

In the given figure, `AB||CD` and `angleAOC=x^(@)`. If `angleOAB=104^(@)` and `angleOCD=116^(@)`, find the value of x.

Text Solution

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Through O draw `OE||AB||CD`. Then, `angleAOE+angleCOE=x^(@)`.
Now, `AB||OE` and AO is the transversal.
`:. angleOAB+angleAOE=180^(@)`
`implies 104^(@) angleAOE=180^(@)`
`implies angleAOE=(180-104)^(@)=76^(@)`.
Again, `CD||OE` and `OC` is the transversal.
`:. angleCOE+angleOCD=180^(@)`
`implies angleCOE+116^(@)=180^(@)`
`implies angleCOE=(180^(@)-116^(@))=64^(@)`.
`:. angleAOC=angleAOE+angleCOE=(76^(@)+64^(@))=140^(@)`.
Hence, `x=140`
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