To determine the number of sides in a polygon based on its interior angle, you can use the formula for the interior angle of a regular polygon: ( \text{Interior angle} = \frac{(n - 2) \times 180}{n} ), where ( n ) is the number of sides. If the interior angle is 10 degrees, you can set up the equation: ( 10 = \frac{(n - 2) \times 180}{n} ). Solving this equation reveals that the polygon would have an infinite number of sides, as a 10-degree angle does not correspond to any finite-sided polygon.
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