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°.

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How do you find the sum of the interior angles of a triangle?

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For a triangle (3 sides), the sum of the interior angles is (3-2) × 180° = 180°.

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

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For a quadrilateral (4 sides), the sum of the interior angles is (4-2) × 180° = 360°.

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

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

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

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For a hexagon (6 sides), the sum of the interior angles is (6-2) × 180° = 720°.

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

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For a heptagon (7 sides), the sum of the interior angles is (7-2) × 180° = 900°.

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What is the sum of the interior angles of an octagon?

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For an octagon (8 sides), the sum of the interior angles is (8-2) × 180° = 1080°.

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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°.

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If one angle of a triangle is 90°, what is the sum of the other two angles?

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The sum of the other two angles in a right triangle is 90°.

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How do you find a missing angle in a polygon?

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To find a missing angle, use the Polygon Angle Sum Theorem to calculate the total sum of angles, then subtract the known angles from that total.