Interior angles are supplementary to exterior angles.  Since it has
some exterior angles of 31°, it has some interior angles of 180°-31° or
149° each.  So there are several possibilities.  For example it could be:

a polygon of 14 sides with 

 6 154° interior angles and  6 26° exterior angles  
 2 171° interior angles and  2  9° interior angles
 6 149° interior angles and  6 31° interior angles
-------------------------------------------------
Sum of interior angles = (n-2)×180° = (14-2)×180° = 12×180° = 2160° 
and 6×154°+2×171°+6×149° = 924°+342°+894° = 2160°. That checks. Also
Sum of exterior angles = 6×26°+2×9°+6×31°=156°+18°+186° = 360°, which
also checks.

Or it could be a polygon of 17 sides with

 7 154° interior angles and  7 26° exterior angles  
 6 171° interior angles and  6  9° interior angles
 4 149° interior angles and  4 31° interior angles
-------------------------------------------------
Sum of interior angles = (n-2)×180° = (17-2)×180° = 15×180° = 2700° 
and 7×154°+6×171°+4×149° = 1078°+1026°+596° = 2700°. That checks. Also
Sum of exterior angles = 7×26°+6×9°+4×31°=182°+54°+124° = 360°, which
also checks.

Or it could be a polygon of 24 sides with

 2 154° interior angles and   2 26° exterior angles  
17 171° interior angles and  17  9° interior angles
 5 149° interior angles and   5 31° interior angles
-------------------------------------------------
Sum of interior angles = (n-2)×180° = (24-2)×180° = 22×180° = 3960° 
and 2×154°+17×171°+5×149° = 308°+2907°+745° = 3960°. That checks. Also
Sum of exterior angles = 2×26°+17×9°+5×31°=52°+153°+155° = 360°, which
also checks.

Or it could be a polygon of 30 sides with

 4 154° interior angles and   4 26° exterior angles  
25 171° interior angles and  25  9° interior angles
 1 149° interior angle  and   1 31° interior angle
-------------------------------------------------
Sum of interior angles = (n-2)×180° = (30-2)×180° = 28×180° = 5040° 
and 4×154°+25×171°+1×149° = 616°+4275°+149° = 5040°. That checks. Also
Sum of exterior angles = 4×26°+25×9°+1×31°=104°+225°+31° = 360°, which
also checks.

So either you've left out some information, or else there are about 6 
or 7 different solutions.  You may discuss it further in the thank-you
note form, and I'll get back to you.

Edwin