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

Options

A. `x=60, y=70, z=60, t=70`
B. `x=70, y=70, z=60, t=60`
C. `x=40, y=50, z=60, t=70`
D. `x=60, y=60, z=70, t=70`

Answer

D

Explanation

`x=60` [vert. opp `angles`] ltbr. `angleQPR=(180^(@)-110^(@))=70^(@)=angleBQS=z^(@)` [corresponding `angles`]
`x^(@)+angleQRS=110^(@)` [alt. int. `angles`] `implies 60^(@)+angleQRS=110^(@)`
`implies angleQRS=50^(@)`.
`x^(@)+angleQRS+t^(2)=180^(@)` [consecutive int. `angles`]
`implies 110^(@)+t^(@)=180^(@) implies t=70`
`y^(@)+angleQRS+t^(@)=180^(@) implies y^(@)+50^(@)+70^(@)=180^(@) implies y=60`.