the sum of the interior angles of a regular polygon is 1260

Answer 1

I am assuming you are asking the number of sides of the regular polygon. The formula for the relationship between number of sides and the sum of the interior angles -- where S is equal to the number of sides -- is (S - 2) x 180. So in this case:

(S - 2) x 180 = 1260

Divide each side by 180:

S - 2 = 1260 / 180 = 7

Then add 2 to find the number of sides:

S = 7 + 2 = 9

The regular polygon has 9 sides. A 9-sided figure is called a nonagon, so it would be called a "Regular Nonagon". The sides would all be equal and the angles would all be an equal 140 degrees, which is 1260 / 9.

Answer 2

If n = number of sides, then 180(n-2) = 1260

So, n - 2 = 7

n = 9

The polygon has 9 sides