SOLUTION: If possible, give the name of the convex polygon in which the sum of the interior angles equals 1260°. hexagon heptagon nonagon no such polygon exists

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Question 322535: If possible, give the name of the convex polygon in which the sum of the interior angles equals 1260°.
hexagon
heptagon
nonagon
no such polygon exists
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Nonagon, 9 sides.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The sum of the interior angles of any convex polygon is:



where is the number of sides (or vertices, for that matter).

So:



and solve for where

If is not an integer, the polygon does not exist. Hint: A hexagon has 6 sides, a heptagon has 7 sides, and a nonagon has 9 sides.

John