it could be something to do with s=(n-2) x 180

\( 180^o-140^o=40^o\\\\360^o:40^o=9\\\\Answer: This\ a\ regular\ polygon\ has\ 9\ sides. \)

Yes, it certainly could ! When you first noticed that formula in a book, or when it was given to you in class, did you also notice or learn what it means?

It means

"The sum of all the interior angles in a polygon" = (number of sides - 2) x 180.

Triangle. 3 sides. (3 - 2) = 1 x 180 = 180° degrees. 60° each if regular

Quadrilateral. 4 sides. (4 - 2) = 2 x 180 = 360° degrees. 90° each if regular

Pentagon. 5 sides. (5 - 2) = 3 x 180 = 540° degrees. 108° each if regular

Hexagon. 6 sides. (6 - 2) = 4 x 180 = 720° degrees. 120° each if regular

Sevenagon. 7 sides. (7 - 2) = 5 x 180 = 900° degrees. 128 and 4/7 each if regular

Octagon. 8 sides. (8 - 2) = 6 x 180 = 1080° degrees. 135° each if regular

Nonagon. **9 sides**. (9 - 2) = 7 x 180 = 1260° degrees. **140° each if regular**