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GRE
GRE Quantitative Reasoning Section

Comparison of Interior and Exterior Angle Sums in a Decagon

Hard Geometry Polygons

Consider a convex polygon with 10 sides (a decagon) where all interior angles are equal. The measure of each interior angle of a regular polygon can be calculated using the formula:

$$ ext{Interior Angle} =\frac{(n - 2) imes 180^ ext{o}}{n}$$

where $$n$$ is the number of sides. Additionally, an exterior angle of a polygon can be calculated as:

$$ ext{Exterior Angle} = 180^ ext{o} - ext{Interior Angle}$$

Using these formulas, calculate the measure of one interior angle and one exterior angle of this decagon. Based on this information, determine the relationship between the sum of the interior angles of the decagon and the sum of its exterior angles.

Hint

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