The sum of the interior angles of a regular polygon A is 1260 degrees and each interior angle of a regular polygon B is 1284/7 degrees. The sum of the number of sides of polygons A and B is:

Answer: Option D

Sum of internal angle = (n - 2) × 180°
Polygon A :
1260° = (n - 2) × 180°
7 = (n - 2)
n = 7 + 2 = 9
Polygon B :
$$\begin{array}{rl}& 180^{\circ }-\frac{{360}^{\circ }}{n}=128\frac{4^{\circ }}{7}\\ & 180^{\circ }-\frac{{360}^{\circ }}{n}=\frac{{900}^{\circ }}{7}\\ & \frac{{360}^{\circ }}{n}=\frac{{1260}^{\circ }-{900}^{\circ }}{7}\\ & \frac{{360}^{\circ }}{n}=\frac{{360}^{\circ }}{7}\\ & n=7\end{array}$$
Sum of Side of polygon A and B = A + B = 9 + 7 = 16