question_answer

In the given figure \[AB||CD,\angle ABE=120{}^\circ ,\angle DCE=100{}^\circ \] AND\[\angle BEC=x{}^\circ \] Then value of x will be

A) 40                                

B) 50

C) 60                                

D) 70

Correct Answer: A

Solution :

If, BM and CN are perpendicular, Then,    \[\angle ABM=90{}^\circ \]and \[\angle DCN=90{}^\circ \] Now,     \[\angle MBE=120{}^\circ -90{}^\circ =30{}^\circ \] And      \[\angle ECN=100-90{}^\circ =10{}^\circ \] So,       \[\angle BEO=\angle MBE=30{}^\circ \] And      \[\angle CEO=\angle ECN=10{}^\circ \] Hence,  \[\angle BEC=x{}^\circ =30{}^\circ +10{}^\circ =40{}^\circ \]