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In the adjoining figure find /x...

In the adjoining figure find `/_x`

Text Solution

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Extend the line CD so that it meets AB at point E
Now, in `Delta AEC`
`angleEAC+angleAEC+angleAC180^(@)` (Angle sum property)

`rArr 54^(@)+angleAEC+38^(@)=180^(@)`
`rArr angle AEC=88^(@)`
In `DeltaBED`
`angle AED=angle+angleEDB` (exterior angle = sum of two opposite interior angles
`rArr angleEDB=88^(@)-43^(@)`
or `angle EDB=45^(@)`
`angleEDB+angleBDC=180^(@)" "(L.P.A)`
`rArr 45^(@)+x=180^(@)`
`rArr x=135^(@)`
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