question_answer

If I be the in centre of\[\Delta ABC\]and\[\angle B={{70}^{o}}\,\,\text{and}\]\[\angle C={{50}^{o}}\], then the magnitude of \[\angle BIC\]is

A) \[{{130}^{o}}\]                                  

B) \[{{60}^{o}}\]

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

D)        \[{{105}^{o}}\]

Correct Answer: C

Solution :

            \[\angle IBC=\frac{{{70}^{o}}}{2}={{35}^{o}}\];             \[\angle ICB=\frac{{{50}^{o}}}{2}={{25}^{o}}\]; \[\therefore \]      \[\angle BIC={{180}^{o}}-{{35}^{o}}-{{25}^{o}}\]             \[={{180}^{o}}-{{60}^{o}}\]             \[={{120}^{o}}\]