In general, the sum of the measures of an n-gon is 180*(n-2).
If we let x equal the number of angles that are 200 degrees, then the sum of the angles in this particular polygon is 6*90 + 200x.
Knowing that x = n-6, we can set the two above expressions equal to one another, so that 6*90 +200*(n-6) = 180*(n-2). Solving for n gives us 15.
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