The sum of the interior angles of a regular polygon A is 1260 degrees and each interior angle of a regular polygon B is $$128\frac{4}{7}$$  degrees. The sum of the number of sides of polygons A and B is:

Solution(By Examveda Team)

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