question_answer

ABC is a triangle in which AB = AC. Let BC be produced to D. From a point E on the line AC let EF be a straight line such that EF is parallel to AB Consider the quadrilateral ECDF thus formed: If \[\angle ABC=65{}^\circ \] and \[\angle EFD=80{}^\circ ,\]then what is the value of \[\angle FDC?\]

A)  \[43{}^\circ \]

B)  \[41{}^\circ \]

C)  \[37{}^\circ \]

D)  \[35{}^\circ \]

Correct Answer: D

Solution :

Here, \[\angle B=\angle C=65{}^\circ \] \[\angle 1=\angle B=65{}^\circ \]           (Corresponding angle) In \[\Delta FGD,\] \[\angle 1+\angle F+\angle D=180{}^\circ \] \[65{}^\circ +80{}^\circ +\angle D=180{}^\circ \] \[\Rightarrow \]               \[\angle D=35{}^\circ \]