In the given figure, ABCD is a square. A line segment DX cuts the side BC at X and the diagonal AC at O such that `angle COD = 105^(@) and angle OXC = x`. The value of x is

Explanation

The angle of a square are bisected by the diagonals.
`therefore angle OCX= 45^(@) [because angle DCB=90^(@) and CA " bisects " angle DCB].`
Also, `angle COD + angle COX=180^(@) " (linear pair)" `
`rArr 105^(@) + angle COX=180^(@) rArr angle COX =(180^(@)-105^(@))=75^(@).`
Now, in `triangle COX,` we have
`angle OCX + angle COX + angle OXC=180^(@)`
`rArr 45^(@)+75^(@)+angle OXC=180^(@) rArr angle OXC=(180^(@)-120^(@))=60^(@).`
Hence, `x=60.`