In the given figure, `AB||CD, angleBAE=50^(@), angleAEC=x^(@)` and `angleECD=100^(@)`. Find the value of x.

Options

A. `x=70`
B. `x=60`
C. `x=50`
D. `x=40`

Answer

C

Explanation

Through E, draw a line `GEH||AB||CD`.
Now, `GE||AB` and EA is the transversal.
`:. angleGEA=angleEAB=50^(@)` [alt. int. `angles`].
Again, `EH||CD` and EC is the transversal.
`:. angleHEC+angleECD=180^(@)` [co. int. `angles`]
`implies angleHEC+100^(@)=180^(@) implies angleHEC=80^(@)`.
Now, GEH si a straight line.
`:. angleGEA+angleAEC+angleHEC=180^(@)` [staight angle]
`implies 50^(@)+x^(@)+80^(@)=180^(@) implies x^(@)=50^(@)`.
Hence, `x=50`.