question_answer

If O is the orthocenter of the \[\Delta \,ABC\]and \[\angle BAC=80{}^\circ ,\] then measure of \[\angle BOC\]is

A) \[80{}^\circ \]

B) \[100{}^\circ \]

C) \[120{}^\circ \]

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

Correct Answer: B

Solution :

[b] From figure, sum of angles of quadrilateral \[ADOE=360{}^\circ \] \[\Rightarrow \]   \[80{}^\circ +90{}^\circ +90{}^\circ +\angle DOE=360{}^\circ \] \[\Rightarrow \]   \[\angle DOE=360{}^\circ -(80{}^\circ +90{}^\circ +90{}^\circ )\] \[=100{}^\circ \] \[\therefore \]      \[\angle BOC=\angle DOE=100{}^\circ \] \[\therefore \]      \[\angle BOC=\angle DOE=100{}^\circ \]