The T.
asked • 02/26/16Polygon Sides
The number of sides of a convex polygon if the sum of the measures of its interior angles is 2,700?
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1 Expert Answer
The sum of interiors angles of any polygon is given by the formula...
"Si=(n-2)180" where...
Si=sum of all interior angles
n=number of sides of a polygon
So let's substitute into the formula and solve for"n"...
Si=(n-2)180.....original formula from above
2700=(n-2)180...substitute for "Si"
15=n-2............divide both sides by 180
17=n...............add 2, both sides
∴ n=17
Therefore, the sum of the interior angles of a polygon with 17 sides is 2700 degrees.
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Norbert J. M.
02/26/16