If in a $$\triangle$$ABC, the bisectors of $$\angle$$B and $$\angle$$C meet at O, inside the triangle. If $$\angle$$BOC = $$156^\circ$$ , then the measure of $$\angle$$A 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 = $$\frac{\angle \text{C}}{2}$$

$$=$$>  $$\angle$$B = 2$$\angle$$OBC  and  $$\angle$$C = 2$$\angle$$OCB

In $$\triangle$$OBC,

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

$$=$$>  156$$^{\circ\ }$$ + $$\angle$$OBC + $$\angle$$OCB = 180$$^{\circ\ }$$

$$=$$>  $$\angle$$OBC + $$\angle$$OCB = 180$$^{\circ\ }$$- 156$$^{\circ\ }$$

$$=$$>  $$\angle$$OBC + $$\angle$$OCB =  24$$^{\circ\ }$$ ..................(1)

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

$$=$$>  $$\angle$$A + 2$$\angle$$OBC + 2$$\angle$$OCB  = 180$$^{\circ\ }$$

$$=$$>  $$\angle$$A + $$2\left(\angle \text{OBC}+\angle \text{OCB}\right)$$ = 180$$^{\circ\ }$$

$$=$$>  $$\angle$$A + $$2\left(24^{\circ\ }\right)$$ = 180$$^{\circ\ }$$

$$=$$>  $$\angle$$A = 180$$^{\circ\ }$$- 48$$^{\circ\ }$$

$$=$$> $$\angle$$A = $$132^\circ$$

Hence, the correct answer is Option A