As C is the centre of the circle above, so $\(\mathrm{AC}=\mathrm{BC}=\)$ radii of the circle which implies $\(\angle \mathrm{BAC}=\angle \mathrm{ABC}=50^{\circ}\)$ (In a triangle when sides are equal, the opposite angles are also equal)



As sum of the angles of a triangle is 180 degrees, in triangle $\(A B C\)$, we get $\(\angle \mathrm{BAC}+\angle \mathrm{ABC}+\angle \mathrm{ACB}=50^{\circ}+50^{\circ}+\angle \mathrm{ACB}=180^{\circ} \Rightarrow \angle \mathrm{ACB}=180^{\circ}-100^{\circ}=80^{\circ}\)$

Hence the angle subtended by the minor arc AB at the centre C i.e. $\(\angle \mathrm{ACB}=80^{\circ}\)$, so the answer is (B).