In the given figure, `AB`||`CD`. Find the values of `x, y` and `z.`

Options

A. `x=110, y=55, z=65`
B. `x=115, y=65, z=60`
C. `x=100, y=70, z=55`
D. `x=105, y=75, z=50`

Answer

D

Explanation

As we can see from the figure

`75^(@)=y^(@)" "` [Alternate interior angles]
`implies y=75`.
Now, `angleEGF+angleEGD=180^(@)" "`[Straight line]
` implies angleEGF+125^(@)=180^(@) implies angleEGF=55^(@)`.
Now, `z^(@)+y^(@)+55^(@)=180^(@)" "`[Sum of angles of a triangle]
` implies z+75+55=180 implies z=50`.
Now, `x+y=180^(@)"
"`[Straight line]
` implies x+75=180 implies x=105`.
`:. x=105, y=75` and `z=50`