Polygon Sum Theorem

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What is the Polygon Sum Theorem?

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

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

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

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What is the measure of a single interior angle in a regular polygon?

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The measure of a single interior angle in a regular polygon can be calculated using the formula: 180(n−2) ÷ n.

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What is the measure of a single exterior angle in a regular polygon?

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The measure of a single exterior angle in a regular polygon can be calculated using the formula: 360 ÷ n, where n is the number of sides.

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What is the sum of 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.

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What is the sum of interior angles for a triangle?

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

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What is the sum of interior angles for a quadrilateral?

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The sum of interior angles for a quadrilateral is 360 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 interior angles for an octagon (8 sides) is 180(8−2) = 1080 degrees.

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If a polygon has 5 sides, what is the measure of a single interior angle in a regular pentagon?

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The measure of a single interior angle in a regular pentagon is 180(5−2) ÷ 5 = 108 degrees.

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

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The measure of a single exterior angle in a dodecagon (12 sides) is 360 ÷ 12 = 30 degrees.