Polygon Angle Sum Theorem

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What is the Polygon Angle Sum Theorem?

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The Polygon Angle Sum Theorem states that the sum of the interior angles of a polygon with n sides is given by the formula: (n - 2) × 180°.

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How do you find the measure of one exterior angle of a regular polygon?

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To find the measure of one exterior angle of a regular polygon, use the formula: 360° / n, where n is the number of sides.

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What is the measure of one interior angle in a regular polygon with n sides?

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The measure of one interior angle in a regular polygon can be calculated using the formula: ((n - 2) × 180°) / n.

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If a polygon has 10 sides, what is the sum of its interior angles?

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The sum of the interior angles of a decagon (10 sides) is (10 - 2) × 180° = 1440°.

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What is the relationship between interior and exterior angles of a polygon?

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The interior and exterior angles of a polygon are supplementary, meaning they add up to 180°.

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How many sides does a polygon have if the measure of one exterior angle is 30°?

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To find the number of sides, use the formula: n = 360° / exterior angle. For 30°, n = 360° / 30° = 12 sides.

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What does 'n' represent in the Polygon Interior Angle Sum Theorem?

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In the Polygon Interior Angle Sum Theorem, 'n' represents the number of sides of the polygon.

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Calculate the measure of one interior angle of a regular hexagon.

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For a hexagon (6 sides), the measure of one interior angle is ((6 - 2) × 180°) / 6 = 120°.

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What is the sum of the exterior angles of any polygon?

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The sum of the exterior angles of any polygon is always 360°, regardless of the number of sides.

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Find the measure of one interior angle in a regular 25-gon.

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The measure of one interior angle in a regular 25-gon is ((25 - 2) × 180°) / 25 = 165.6°.