The sum of the INterior angles of a n-sided polygon is given
by the formula;

     (n-2)×180° = the sum of the n INterior angles.

A nonagon has 9 sides, so we substitute 9 for n:

     (9-2)×180° = the sum of the 9 INterior angles.
         7×180° = the sum of the 9 INterior angles.
          1260° = the sum of the 9 INterior angles.

Since the nonagon is a REGULAR nonagon, all of the INterior
angles are equal, and since there are 9 of them, we divide the
1260° by 9 and get 140° for each of the INterior angles.

---------------------------------------------------------------

The sum of the EXterior angles of every polygon is

     360° = the sum of the 9 EXterior angles. 

Since the nonagon is a REGULAR nonagon, all of the EXterior
angles are equal, and since there are 9 of them, we divide the
360° by 9 and get 40° for each of the EXterior angles.
 
Edwin