SOLUTION: The sum of the interior angles of two polygons is 1440 degrees and the sum of their diagonals is 19. What is the sum of the sides of the two polygons and the sum of the exterior an

Algebra ->  Polygons -> SOLUTION: The sum of the interior angles of two polygons is 1440 degrees and the sum of their diagonals is 19. What is the sum of the sides of the two polygons and the sum of the exterior an      Log On


   

Question 1142820: The sum of the interior angles of two polygons is 1440 degrees and the sum of their diagonals is 19. What is the sum of the sides of the two polygons and the sum of the exterior angles of two polygons? Thanks.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


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.
  # sides  # diagonals (n(n-3)/2)
 ---------------------------------
     3       0
     4       2
     5       5
     6       9
     7      14
     8      20


The only two numbers of diagonals that sum to 19 are 5 and 14, for a pentagon and a heptagon.

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.