Question 1142820
<br>
The numbers are small; solve by looking at the numbers of diagonals of polygons, rather than using algebraic formulas for the measures of interior angles of polygons.<br><pre>
  # sides  # diagonals (n(n-3)/2)
 ---------------------------------
     3       0
     4       2
     5       5
     6       9
     7      14
     8      20</pre><br>
The only two numbers of diagonals that sum to 19 are 5 and 14, for a pentagon and a heptagon.<br>
The sum of the measures of the interior angles of a pentagon and a heptagon should add up to 1440 degrees; otherwise the problem is defective.