question_answer

Two parallel lines AB and CD are intersected by a transversal line EF at M and N respectively. The lines MP and NP are the bisectors of the interior angles \[\angle BMN\]and \[\angle DNM\]on the same side of the transversal. Then,\[\angle MPN\]is equal to

A)  \[90{}^\circ \] 

B)  \[45{}^\circ \]

C) \[135{}^\circ \]

D)  \[60{}^\circ \]

Correct Answer: A

Solution :

As,        \[\angle BMN+\angle DNM=180{}^\circ \] \[\angle PMN+\angle PNM=90{}^\circ \] \[\angle MPN=180{}^\circ -(\angle PMN+\angle PNM)=180{}^\circ -90{}^\circ \] \[\Rightarrow \]   \[\angle MPN=90{}^\circ \]