In a $$\triangle$$ABC,the bisectors of $$\angle$$B and $$\angle$$C meet at O with in the triangle. If $$\angle$$A = 110$$^\circ$$, then the measure of $$\angle$$BOC is:

From the figure,

OB and OC are angular bisectors of $$\angle$$B and $$\angle$$C

$$=$$>  $$\angle$$OBC = $$\frac{\angle \text{B}}{2}$$  and  $$\angle$$OCB = $$\frac{\angle \text{C}}{2}$$

In $$\triangle$$ABC,

$$\angle$$A + $$\angle$$B + $$\angle$$C = 180$$^{\circ\ }$$

$$=$$>  110$$^{\circ\ }$$ + $$\angle$$B + $$\angle$$C = 180$$^{\circ\ }$$

$$=$$>  $$\angle$$B + $$\angle$$C = 180$$^{\circ\ }$$ - 110$$^{\circ\ }$$

$$=$$>  $$\angle$$B + $$\angle$$C = 70$$^{\circ\ }$$ ......................(1)

In $$\triangle$$OBC,

$$\angle$$BOC + $$\angle$$OBC + $$\angle$$OCB = 180$$^{\circ\ }$$

$$=$$>  $$\angle$$BOC + $$\frac{\angle \text{B}}{2}$$ + $$\frac{\angle \text{C}}{2}$$ = 180$$^{\circ\ }$$

$$=$$>  $$\angle$$BOC + $$\frac{\angle \text{B}+\angle \text{C}}{2}$$ = 180$$^{\circ\ }$$

$$=$$>  $$\angle$$BOC + $$\frac{70^{\circ\ }}{2}$$ = 180$$^{\circ\ }$$

$$=$$> $$\angle$$BOC = 180$$^{\circ\ }$$- 35$$^{\circ\ }$$

$$=$$> $$\angle$$BOC = 145$$^{\circ\ }$$

Hence, the correct answer is Option C