To determine the exterior angle formed when one side of a pentagon is extended, we can utilize the relationship between the interior and exterior angles of polygons.
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Understanding the Polygon: A regular pentagon has 5 sides. The sum of the interior angles of a polygon is given by the formula: \[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \] where \( n \) is the number of sides. For a pentagon (\( n = 5 \)): \[ \text{Sum of interior angles} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ \]
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Calculating One Interior Angle: If the pentagon is regular (all sides and angles are equal), each interior angle is: \[ \text{Interior angle} = \frac{540^\circ}{5} = 108^\circ \]
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Finding the Exterior Angle: The exterior angle at a vertex of the polygon is supplementary to the interior angle, meaning they add up to \( 180^\circ \): \[ \text{Exterior angle} = 180^\circ - \text{Interior angle} \] For each interior angle of \( 108^\circ \): \[ \text{Exterior angle} = 180^\circ - 108^\circ = 72^\circ \]
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As the Line is Extended: When you extend one of the sides of the pentagon, you essentially create one of the exterior angles. So, regardless of whether it’s the interior or exterior angle you initially consider, extending one side also results in an exterior angle equal to \( 72^\circ \).
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Conclusion: The angle of the exterior angle formed where the line is extended is \( 72^\circ \).