Question 196331
Start with the formula for the sum of the interior angles of a polygon with n sides: {{{S = (n-2)*(180)}}}
In the problem, this sum is given as 1260 degrees, so...
{{{(n-2)*(180) = 1260}}} Divide both sides by 180
{{{n-2 = 7}}} Add 2 to both sides.
{{{n = 9}}} The polygon has 9 sides (Called a nonagon)
The size of each interior angle of a regular polygon is given by: {{{A = ((n-2)*(180))/n}}}, so...
{{{A = 1260/9}}}
{{{A = 140}}}degrees.