Question 560370
The sum (S) of the interior angles of a polygon of n sides is given by:
{{{S = (n-2)180}}} and S is given as 1440 so...
{{{(n-2)180 = 1440}}} Divide both sides by 180.
{{{n-2 = 8}}} Add 2 to both sides.
{{{n = 10}}} The regular polygon has 10 sides.
An interior angle (A) of a regular polygon of n sides is given by:
{{{A = (n-1)180/n}}} But {{{(n-2)180 = 1440}}} and n = 10:
{{{A = 1440/10}}}
{{{A = 144}}}degrees.