In figure if `AB||CD`,`CD||EF` and `y: z = 3: 7`, find `x`.

Options

A. `x=26^(@)`
B. `x=120^(@)`
C. `x=126^(@)`
D. `x=106^(@)`

Answer

C

Explanation

`y:x=3:7`
`y=3k,z=7k`
`x=angleCHG" "` (crosseponding angles ).....(1)
But `angleCHG=z " `" (alternate angles) ....(2)
`:.` From (1) and (2), we get
`x=z " ".....(3)`
`x+y=180^(@) " "` (sum of co-int angles)
`7k+3k=180^(@)" "` [ from (3)]
`10k =180^(@)`
`k=18^(@)`
`y=3xx18^(@)=54^(@)`
`z=7xx18^(@)=126^(@)`
x=z
`:. x=126^(@)`