Polygon Angle Sum Theorem

Front

What is the Polygon Angle Sum Theorem?

Back

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°.

Front

How do you calculate the sum of the interior angles of a polygon with 16 sides?

Back

Using the formula (n - 2) × 180°, for n = 16: (16 - 2) × 180° = 2520°.

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What is the measure of one interior angle of a regular polygon with 16 sides?

Back

The measure of one interior angle of a regular polygon is calculated by dividing the sum of the interior angles by the number of sides: 2520° / 16 = 157.5°.

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How do you find the number of sides of a polygon if the sum of its interior angles is 2700°?

Back

Use the formula (n - 2) × 180° = 2700°. Solving gives n = 17 sides.

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What is the measure of one exterior angle of a regular decagon?

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The measure of one exterior angle of a regular polygon is calculated by dividing 360° by the number of sides: 360° / 10 = 36°.

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

Back

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

Front

If a polygon has 15 sides, what is the sum of its interior angles?

Back

Using the formula (n - 2) × 180°, for n = 15: (15 - 2) × 180° = 2340°.

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

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For a regular pentagon (5 sides), the sum of the interior angles is (5 - 2) × 180° = 540°. Each interior angle is 540° / 5 = 108°.

Front

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

Back

The measure of one exterior angle of a regular polygon can be found using the formula 360° / n, where n is the number of sides.

Front

What is the sum of the interior angles of a polygon with 11 sides?

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Using the formula (n - 2) × 180°, for n = 11: (11 - 2) × 180° = 1620°.