Make a straight line through a vertex of a polygon, cut off two corners of the polygon, and the sum of its inner angles becomes 1260 degrees, then the original number of sides of the polygon is 1260 degrees______ ．

Make a straight line through a vertex of a polygon, cut off two corners of the polygon, and the sum of its inner angles becomes 1260 degrees, then the original number of sides of the polygon is 1260 degrees______ ．

Because 1260 = 7 × 180, it is now a 7 + 2 = 9-sided polygon. A vertex of a polygon makes a straight line and cuts off two corners of the polygon. There are two cases: first, if the line passes through another vertex, three edges are reduced and one edge is added. In total, two edges are reduced, which turns out to be 9 + 2 = 11; second, if the line does not pass through other vertices, only two edges are reduced, The other one is just a little shorter, but it's still an edge. Add another edge and reduce one edge altogether. The original number is 9 + 1 = 10. In conclusion, the original number of edges is 11 or 10, so fill in: 10 or 11