The formula usually used for the sum of interior angles of an n-sided convex polygon is ...
... angle sum = 180°×(n -2)
In your case, angle sum is 900°, so this becomes
... 900 = 180(n -2)
... 5 = n -2 . . . . . . . . . divide by 180
... 7 = n . . . . . . . . . . . the polygon has 7 sides
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It may be easy to remember that the sum of exterior angles is always 360°, and each exterior angle adds to its corresponding interior angle to make 180°. Then, for n angles The sum of interior and exterior angles is n·180°. Subtracting the sum of exterior angles from this gives the sum of interior angles: n·180° -360° = 180°(n-2).
