question_answer

In the following figure, \[AC||BD,\]and \[\angle CAF=25{}^\circ ,\]\[\angle DBG=65{}^\circ \]and \[BF=BA.\] Then, \[\angle BFE\]is equal to

A) \[90{}^\circ \]                          

B) \[155{}^\circ \]

C) \[140{}^\circ \]

D) \[165{}^\circ \]

Correct Answer: C

Solution :

Since, \[BF=BA\]

\[\therefore \]      \[\angle 1+25{}^\circ =65{}^\circ \]      [since, \[AC||BD\]]

\[\Rightarrow \]   \[\angle 1=65{}^\circ -25{}^\circ =40{}^\circ \]

\[\angle 1=\angle 2=40{}^\circ \] [as \[BF=BA\]]

\[\angle 2+\angle x=180{}^\circ \]  [supplementary angles]

\[\Rightarrow \]   \[\angle x=140{}^\circ \]