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 (n - 2) × 180 degrees.

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How do you calculate the sum of the interior angles of a polygon?

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The sum of the interior angles of a polygon can be calculated using the formula (n - 2) × 180, where n is the number of sides.

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What is the formula to find one interior angle in a regular polygon?

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To find one interior angle in a regular polygon, use the formula ((n - 2) × 180) / n.

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What is the formula to find one exterior angle in a regular polygon?

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The formula to find one exterior angle in a regular polygon is 360/n, where n is the number of sides.

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If a polygon has 8 sides, what is the sum of its interior angles?

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The sum of the interior angles of an 8-sided polygon is (8 - 2) × 180 = 1080 degrees.

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If a polygon has 12 sides, what is the measure of one exterior angle?

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The measure of one exterior angle of a 12-sided polygon is 360/12 = 30 degrees.

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What is the measure of one interior angle of a regular pentagon?

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The measure of one interior angle of a regular pentagon is ((5 - 2) × 180) / 5 = 108 degrees.

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How many sides does a polygon have if the sum of its interior angles is 720 degrees?

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A polygon with a sum of interior angles of 720 degrees has 8 sides, since (n - 2) × 180 = 720 leads to n = 8.

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

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

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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 degrees, regardless of the number of sides.