Question 1062720: The sum of the measure of the interior angles of a polygon is 1800 degrees. Determine the number of sides for the polygon.
Found 2 solutions by addingup, KMST:
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! You have to use the formula for the sum of the interior angles, n, of a polygon.
:
(n-2)180° = sum of the angles.
In this problem:
(n-2)180 = 1800
n-2 = 10
n = 12
So, you have a 12-sided polygon which is called a DODECAGON
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! 
Relying on formulas, you would have memorized that,
for a polygon with  sides, that sum is
 ,
and in this case
 ----> .
Relying on ideas, you would remember how, in a convex polygon,
all the diagonals drawn from one vertex divide it into triangles
(two less triangles than the number of sides);
the angles of those triangles are the interior angles of the polygon,
and that, with a sum of  per triangle, you would have
 triangles.
Or maybe you would think of those incredibly useful exterior angles.
The exterior angles measure how much your direction changes at each vertex as you go around the polygon.
Of course, each exterior angle is attached to an exterior angle,
and they are supplementary, meaning that the pair of angles adds to .
All the exterior angles add up to a whole turn around the polygon;
 .
For the polygon in this question, the sum of all exterior and interior angles is
 .
That means  interior-exterior pairs,
meaning angles in that polygon.
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