question_answer

     In the figure given above, ABCD is a trapezium EF is parallel to AD and BC. \[\angle \,\,y\] is equal to       

A)  \[30{}^\circ \]                         

B)  \[45{}^\circ \]

C)  \[60{}^\circ \] 

D)  \[65{}^\circ \]

Correct Answer: C

Solution :

From figure, \[x{}^\circ =z{}^\circ =50{}^\circ \](alternate interior angles) \[\theta +z{}^\circ =180{}^\circ \](linear pair) \[\theta =180{}^\circ -150{}^\circ =130{}^\circ \] Now, in quadrilateral AQFD, \[x{}^\circ +y{}^\circ +120{}^\circ +\theta =360{}^\circ \] \[\Rightarrow \]\[50{}^\circ +y{}^\circ +120{}^\circ +130{}^\circ =360{}^\circ \] \[\therefore \]\[y=360{}^\circ -300{}^\circ =60{}^\circ \]