question_answer

In the  given figure AB ||CD and \[\angle BAE=110{}^\circ ,\]\[\angle ECD=120{}^\circ \] and \[\angle AEC=x{}^\circ .\]Then, the value of x is

A)  \[70{}^\circ \] 

B)  \[105{}^\circ \]

C)  \[120{}^\circ \]

D)  \[130{}^\circ \]

Correct Answer: D

Solution :

Draw FEG || AB || CD AB ||EG and AE is the transversal                 \[\therefore \]\[\angle BAE+\angle AEG=180{}^\circ \Rightarrow 110{}^\circ +\angle AEG=180{}^\circ \] \[\angle AEG=70{}^\circ \] Again, EG||CD and EC is the transversal \[\therefore \]      \[\angle GEC+\angle ECD=180{}^\circ \] \[\Rightarrow \]   \[\angle GEC+120{}^\circ \]\[\Rightarrow \]\[180{}^\circ \] \[\Rightarrow \]   \[\angle GEC=60{}^\circ \] \[\therefore \]      \[x=70{}^\circ +60{}^\circ =130{}^\circ \]