question_answer

In the given figure \[AB||CD,\]\[\angle ABE=120{}^\circ ,\]\[\angle DCE=100{}^\circ \] and \[\angle BEC=x{}^\circ .\] Then, the measurement of x is     

A)  \[15{}^\circ \]                         

B)  \[40{}^\circ \]

C)  \[45{}^\circ \]                         

D)  None of these

Correct Answer: B

Solution :

Through the point E, draw GEH ||AB || CD. AB| | GE and BE is the transversal. \[\therefore \]      \[\angle ABE+\angle GEB=180{}^\circ \] \[\Rightarrow \]   \[120{}^\circ +\angle GEB=180{}^\circ \] \[\therefore \]                  \[\angle GEB=60{}^\circ \] Again, CD| | EH and CE is the transversal. \[\therefore \]      \[\angle DCE+\angle CEH=180{}^\circ \] \[\Rightarrow \]               \[\angle CEH=180{}^\circ \] Now, \[\angle GEB+\angle BEC+\angle CEH=180{}^\circ \] \[\Rightarrow \]   \[60{}^\circ +x+80{}^\circ =180{}^\circ \] \[\Rightarrow \]               \[x=40{}^\circ \]