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) 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 180(n−2), where n is the number of sides.

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What is the formula for the sum of exterior angles in 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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If a regular polygon has an interior angle of 120 degrees, how many sides does it have?

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A regular polygon with an interior angle of 120 degrees has 6 sides.

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What is the formula for finding 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 found using the formula 180(n−2)÷n, where n is the number of sides.

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What is the relationship between the 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 degrees.

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

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The measure of an exterior angle of a regular polygon can be found using the formula 360/n, 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 always 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 always 360 degrees.

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How can you determine the number of sides in a polygon if you know the sum of its interior angles?

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You can determine the number of sides in a polygon by rearranging the formula for the sum of interior angles: n = (sum of interior angles + 360) / 180.