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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To calculate the sum of the interior angles of a polygon, use the formula: (n - 2) × 180, where n is the number of sides.

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What is the sum of the interior angles of a triangle?

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The sum of the interior angles of a triangle is 180 degrees.

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What is the sum of the interior angles of a quadrilateral?

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The sum of the interior angles of a quadrilateral is 360 degrees.

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If a polygon has 5 sides, what is the sum of its interior angles?

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The sum of the interior angles of a 5-sided polygon (pentagon) is (5 - 2) × 180 = 540 degrees.

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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 (octagon) is (8 - 2) × 180 = 1080 degrees.

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How many sides does a polygon have if the sum of its interior angles is 900 degrees?

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A polygon with a sum of interior angles of 900 degrees has 7 sides.

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What is the relationship between the number of sides and the sum of the interior angles?

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The relationship is given by the formula: Sum of interior angles = (n - 2) × 180, where n is the number of sides.

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What is the sum of the interior angles of a nonagon?

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The sum of the interior angles of a nonagon (9 sides) is (9 - 2) × 180 = 1260 degrees.

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If the sum of the interior angles of a polygon is 1440 degrees, how many sides does it have?

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A polygon with a sum of interior angles of 1440 degrees has 10 sides.