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Only when it is a regular polygon that all interior angles are of equal measure
The formula for the sum of the measures of the interior angles of a regular polygon is (n-2)180. Set this equal to 900 and solve for n to find the number of sides in the polygon. 900 = 180(n-2) 900 = 180n - 360 180n = 1260 n = 1260/180 n = 7
7
A formula for this question is that the total measure of the interior angles of a polygon is 180 degrees multiplied by 2 less than the number of sides. For a seven sided polygon, this formula yields 180 X 5 = 900 degrees.
Only if the polygon is "regular".